Статті в журналах: "Algorithme split"

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Ortiz Díaz, Agustín Alejandro, Isvani Inocencio Frías Blanco, Laura María Palomino Mariño, and Fabiano Baldo. "An Online Tree-Based Approach for Mining Non-Stationary High-Speed Data Streams." Revista de Informática Teórica e Aplicada 27, no. 1 (January 15, 2020): 36–47. http://dx.doi.org/10.22456/2175-2745.90822.

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This paper presents a new learning algorithm for inducing decision trees from data streams. In these domains, large amounts of data are constantly arriving over time, possibly at high speed. The proposed algorithm uses a top-down induction method for building trees, splitting leaf nodes recursively, until none of them can be expanded. The new algorithm combines two split methods in the tree induction. The first method is able to guarantee, with statistical significance, that each split chosen would be the same as that chosen using infinite examples. By doing so, it aims at ensuring that the tree induced online is close to the optimal model. However, this split method often needs too many examples to make a decision about the best split, which delays the accuracy improvement of the online predictive learning model. Therefore, the second method is used to split nodes more quickly, speeding up the tree growth. The second split method is based on the observation that larger trees are able to store more information about the training examples and to represent more complex concepts. The first split method is also used to correct splits previously suggested by the second one, when it has sufficient evidence. Finally, an additional procedure rebuilds the tree model according to the suggestions made with an adequate level of statistical significance. The proposed algorithm is empirically compared with several well-known induction algorithms for learning decision trees from data streams. In the tests it is possible to observe that the proposed algorithm is more competitive in terms of accuracy and model size using various synthetic and real world datasets.

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2

García-Martín, Eva, Niklas Lavesson, Håkan Grahn, Emiliano Casalicchio, and Veselka Boeva. "Energy-aware very fast decision tree." International Journal of Data Science and Analytics 11, no. 2 (March 2021): 105–26. http://dx.doi.org/10.1007/s41060-021-00246-4.

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AbstractRecently machine learning researchers are designing algorithms that can run in embedded and mobile devices, which introduces additional constraints compared to traditional algorithm design approaches. One of these constraints is energy consumption, which directly translates to battery capacity for these devices. Streaming algorithms, such as the Very Fast Decision Tree (VFDT), are designed to run in such devices due to their high velocity and low memory requirements. However, they have not been designed with an energy efficiency focus. This paper addresses this challenge by presenting the nmin adaptation method, which reduces the energy consumption of the VFDT algorithm with only minor effects on accuracy. nmin adaptation allows the algorithm to grow faster in those branches where there is more confidence to create a split, and delays the split on the less confident branches. This removes unnecessary computations related to checking for splits but maintains similar levels of accuracy. We have conducted extensive experiments on 29 public datasets, showing that the VFDT with nmin adaptation consumes up to 31% less energy than the original VFDT, and up to 96% less energy than the CVFDT (VFDT adapted for concept drift scenarios), trading off up to 1.7 percent of accuracy.

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3

Liang, Liang. "A Fusion Multiobjective Empire Split Algorithm." Journal of Control Science and Engineering 2020 (December 14, 2020): 1–14. http://dx.doi.org/10.1155/2020/8882086.

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In the last two decades, swarm intelligence optimization algorithms have been widely studied and applied to multiobjective optimization problems. In multiobjective optimization, reproduction operations and the balance of convergence and diversity are two crucial issues. Imperialist competitive algorithm (ICA) and sine cosine algorithm (SCA) are two potential algorithms for handling single-objective optimization problems, but the research of them in multiobjective optimization is scarce. In this paper, a fusion multiobjective empire split algorithm (FMOESA) is proposed. First, an initialization operation based on opposition-based learning strategy is hired to generate a good initial population. A new reproduction of offspring is introduced, which combines ICA and SCA. Besides, a novel power evaluation mechanism is proposed to identify individual performance, which takes into account both convergence and diversity of population. Experimental studies on several benchmark problems show that FMOESA is competitive compared with the state-of-the-art algorithms. Given both good performance and nice properties, the proposed algorithm could be an alternative tool when dealing with multiobjective optimization problems.

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4

Jin, C., L. J. Lu, and J. N. Min. "A two-stage construction heuristic approach for vehicle routing problem with split deliveries and pickups: Case studies and performance comparison." Advances in Production Engineering & Management 17, no. 1 (March 15, 2022): 121–33. http://dx.doi.org/10.14743/apem2022.1.425.

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The vehicle routing problem with split deliveries and pickups is a hot research topic in recent years, where a customer can be served multiple times with split deliveries and pickups. The objective is to minimize the travel distance, use the fewest number of vehicles and increase the load rate, which will further reduce the carbon emissions that damage the environment. In this paper, we use a two-stage construction heuristic approach to solve this problem. First, partitioning algorithms based on the multi-restart-iterative sweep algorithm are adopted to partition the customer domain into sub-domains according to the vehicle capacity, and to determine the split points and the corresponding values. Second, a modified Clarke-Wright savings algorithm is used to check the possibility of each point in each route based on the load of each point and the vehicle load limitation. The three case studies with 12 instances per each from the reconstructed Solomon benchmark datasets were conducted to evaluate the effectiveness and feasibility of the proposed approaches-Unsplit, Both-Split and Enhanced-Both-Split. The comparison among these approaches reveals that the splits reduce the total travel cost and vehicles used, and increase the average loading rate considerably, especially when customers have larger demand values. Our computation results proves that the vehicle routing problem with split deliveries and pickups is highly beneficial for transportation and logistics enterprises.

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5

Pinker, Rachel T., Donglian Sun, Meng-Pai Hung, Chuan Li, and Jeffrey B. Basara. "Evaluation of Satellite Estimates of Land Surface Temperature from GOES over the United States." Journal of Applied Meteorology and Climatology 48, no. 1 (January 1, 2009): 167–80. http://dx.doi.org/10.1175/2008jamc1781.1.

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Abstract A comprehensive evaluation of split-window and triple-window algorithms to estimate land surface temperature (LST) from Geostationary Operational Environmental Satellites (GOES) that were previously described by Sun and Pinker is presented. The evaluation of the split-window algorithm is done against ground observations and against independently developed algorithms. The triple-window algorithm is evaluated only for nighttime against ground observations and against the Sun and Pinker split-window (SP-SW) algorithm. The ground observations used are from the Atmospheric Radiation Measurement Program (ARM) Central Facility, Southern Great Plains site (April 1997–March 1998); from five Surface Radiation Budget Network (SURFRAD) stations (1996–2000); and from the Oklahoma Mesonet. The independent algorithms used for comparison include the National Oceanic and Atmospheric Administration/National Environmental Satellite, Data and Information Service operational method and the following split-window algorithms: that of Price, that of Prata and Platt, two versions of that of Ulivieri, that of Vidal, two versions of that of Sobrino, that of Coll and others, the generalized split-window algorithm as described by Becker and Li and by Wan and Dozier, and the Becker and Li algorithm with water vapor correction. The evaluation against the ARM and SURFRAD observations indicates that the LST retrievals from the SP-SW algorithm are in closer agreement with the ground observations than are the other algorithms tested. When evaluated against observations from the Oklahoma Mesonet, the triple-window algorithm is found to perform better than the split-window algorithm during nighttime.

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6

Hidayat, Trifenaus Prabu, and Andre Sugioko. "Performance Analyzes of Bee Colony Split-Plot Algorithm." International Journal of Information and Education Technology 5, no. 7 (2015): 549–52. http://dx.doi.org/10.7763/ijiet.2015.v5.566.

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7

Yang, Bin-Bin, Song-Qing Shen, and Wei Gao. "Weighted Oblique Decision Trees." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5621–27. http://dx.doi.org/10.1609/aaai.v33i01.33015621.

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Decision trees have attracted much attention during the past decades. Previous decision trees include axis-parallel and oblique decision trees; both of them try to find the best splits via exhaustive search or heuristic algorithms in each iteration. Oblique decision trees generally simplify tree structure and take better performance, but are always accompanied with higher computation, as well as the initialization with the best axis-parallel splits. This work presents the Weighted Oblique Decision Tree (WODT) based on continuous optimization with random initialization. We consider different weights of each instance for child nodes at all internal nodes, and then obtain a split by optimizing the continuous and differentiable objective function of weighted information entropy. Extensive experiments show the effectiveness of the proposed algorithm.

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8

Bollwein, Ferdinand, and Stephan Westphal. "A branch & bound algorithm to determine optimal bivariate splits for oblique decision tree induction." Applied Intelligence 51, no. 10 (March 12, 2021): 7552–72. http://dx.doi.org/10.1007/s10489-021-02281-x.

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AbstractUnivariate decision tree induction methods for multiclass classification problems such as CART, C4.5 and ID3 continue to be very popular in the context of machine learning due to their major benefit of being easy to interpret. However, as these trees only consider a single attribute per node, they often get quite large which lowers their explanatory value. Oblique decision tree building algorithms, which divide the feature space by multidimensional hyperplanes, often produce much smaller trees but the individual splits are hard to interpret. Moreover, the effort of finding optimal oblique splits is very high such that heuristics have to be applied to determine local optimal solutions. In this work, we introduce an effective branch and bound procedure to determine global optimal bivariate oblique splits for concave impurity measures. Decision trees based on these bivariate oblique splits remain fairly interpretable due to the restriction to two attributes per split. The resulting trees are significantly smaller and more accurate than their univariate counterparts due to their ability of adapting better to the underlying data and capturing interactions of attribute pairs. Moreover, our evaluation shows that our algorithm even outperforms algorithms based on heuristically obtained multivariate oblique splits despite the fact that we are focusing on two attributes only.

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9

Huang, Zheng, Yanting Zhang, Lin Wang, Jingyu Xu, and Yunlong Zheng. "Research on multi-objective parameter optimization of split flow dual flash thermodynamic cycle." Journal of Physics: Conference Series 2728, no. 1 (March 1, 2024): 012008. http://dx.doi.org/10.1088/1742-6596/2728/1/012008.

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Abstract In addition to considering the intermediate pressure variables, the split flow double flash thermodynamic cycle also needs to consider the operating conditions and split flow coefficient of the cycle. Traditional algorithms require too much computation and have a longer response time. Faced with sudden operating conditions or changes in production conditions, it is difficult to quickly re-optimize the intermediate parameters of the split flow double flash thermal cycle and carry out corresponding system control. This article uses intelligent optimization algorithms instead of global search methods to optimize multi-objective parameters in a split flow double flash thermodynamic cycle. By summarizing and analyzing the characteristics of algorithms such as SIO, EA, and ANN, it is believed that the GWO algorithm in the SIO class is the most suitable for multi-objective parameter optimization of the split flow double flash thermal cycle. It is combined with the SA optimization algorithm to propose the SA-GWO algorithm with faster optimization speed and higher optimization accuracy, taking the initial position of the wolf pack as the optimization objective. Combined with the cycle thermodynamic model, a multi-objective parameter optimization model for the split flow double flash thermal cycle is established.

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10

Xiao, Su. "Deblurring by Solving a TVp-Regularized Optimization Problem Using Split Bregman Method." Advances in Multimedia 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/906464.

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Image deblurring is formulated as an unconstrained minimization problem, and its penalty function is the sum of the error term and TVp-regularizers with0<p<1. Although TVp-regularizer is a powerful tool that can significantly promote the sparseness of image gradients, it is neither convex nor smooth, thus making the presented optimization problem more difficult to deal with. To solve this minimization problem efficiently, such problem is first reformulated as an equivalent constrained minimization problem by introducing new variables and new constraints. Thereafter, the split Bregman method, as a solver, splits the new constrained minimization problem into subproblems. For each subproblem, the corresponding efficient method is applied to ensure the existence of closed-form solutions. In simulated experiments, the proposed algorithm and some state-of-the-art algorithms are applied to restore three types of blurred-noisy images. The restored results show that the proposed algorithm is valid for image deblurring and is found to outperform other algorithms in experiments.

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11

Zhao, Jing, and Hang Zhang. "Solving Split Common Fixed-Point Problem of Firmly Quasi-Nonexpansive Mappings without Prior Knowledge of Operators Norms." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/389689.

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Very recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms for the split common fixed-point problem concerned two bounded linear operators. However, to employ Moudafi’s algorithms, one needs to know a prior norm (or at least an estimate of the norm) of the bounded linear operators. To estimate the norm of an operator is very difficult, if it is not an impossible task. It is the purpose of this paper to introduce a viscosity iterative algorithm with a way of selecting the stepsizes such that the implementation of the algorithm does not need any prior information about the operator norms. We prove the strong convergence of the proposed algorithms for split common fixed-point problem governed by the firmly quasi-nonexpansive operators. As a consequence, we obtain strong convergence theorems for split feasibility problem and split common null point problems of maximal monotone operators. Our results improve and extend the corresponding results announced by many others.

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Zhu, Wei, Shi Shu, and Lizhi Cheng. "An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration." Advances in Applied Mathematics and Mechanics 6, no. 2 (April 2014): 145–64. http://dx.doi.org/10.4208/aamm.2013.m175.

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AbstractIn this paper, we propose a fast proximity point algorithm and apply it to total variation (TV) based image restoration. The novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation (TV) based image restoration have been proposed. Many current algorithms for TV-based image restoration, such as Chambolle’s projection algorithm, the split Bregman algorithm, the Bermúdez-Moreno algorithm, the Jia-Zhao denoising algorithm, and the fixed point algorithm, can be viewed as special cases of the new first-order schemes. Moreover, the convergence of the new algorithm has been analyzed at length. Finally, we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at present. Numerical experiments illustrate the efficiency of the proposed algorithms.

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Chen, Ying-ping, and Chao-Hong Chen. "Enabling the Extended Compact Genetic Algorithm for Real-Parameter Optimization by Using Adaptive Discretization." Evolutionary Computation 18, no. 2 (June 2010): 199–228. http://dx.doi.org/10.1162/evco.2010.18.2.18202.

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An adaptive discretization method, called split-on-demand (SoD), enables estimation of distribution algorithms (EDAs) for discrete variables to solve continuous optimization problems. SoD randomly splits a continuous interval if the number of search points within the interval exceeds a threshold, which is decreased at every iteration. After the split operation, the nonempty intervals are assigned integer codes, and the search points are discretized accordingly. As an example of using SoD with EDAs, the integration of SoD and the extended compact genetic algorithm (ECGA) is presented and numerically examined. In this integration, we adopt a local search mechanism as an optional component of our back end optimization engine. As a result, the proposed framework can be considered as a memetic algorithm, and SoD can potentially be applied to other memetic algorithms. The numerical experiments consist of two parts: (1) a set of benchmark functions on which ECGA with SoD and ECGA with two well-known discretization methods: the fixed-height histogram (FHH) and the fixed-width histogram (FWH) are compared; (2) a real-world application, the economic dispatch problem, on which ECGA with SoD is compared to other methods. The experimental results indicate that SoD is a better discretization method to work with ECGA. Moreover, ECGA with SoD works quite well on the economic dispatch problem and delivers solutions better than the best known results obtained by other methods in existence.

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Li, Meixia, Xueling Zhou, and Wenchao Wang. "Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem." Journal of Function Spaces 2020 (June 3, 2020): 1–15. http://dx.doi.org/10.1155/2020/6034754.

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In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.

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Wang, Xinglong, Jing Zhao, and Dingfang Hou. "Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem." Mathematics 7, no. 2 (January 23, 2019): 119. http://dx.doi.org/10.3390/math7020119.

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The split feasibility problem models inverse problems arising from phase retrievals problems and intensity-modulated radiation therapy. For solving the split feasibility problem, Xu proposed a relaxed CQ algorithm that only involves projections onto half-spaces. In this paper, we use the dual variable to propose a new relaxed CQ iterative algorithm that generalizes Xu’s relaxed CQ algorithm in real Hilbert spaces. By using projections onto half-spaces instead of those onto closed convex sets, the proposed algorithm is implementable. Moreover, we present modified relaxed CQ algorithm with viscosity approximation method. Under suitable conditions, global weak and strong convergence of the proposed algorithms are proved. Some numerical experiments are also presented to illustrate the effectiveness of the proposed algorithms. Our results improve and extend the corresponding results of Xu and some others.

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GEORGE, ALAN D., and KEONWOOK KIM. "PARALLEL ALGORITHMS FOR SPLIT-APERTURE CONVENTIONAL BEAMFORMING." Journal of Computational Acoustics 07, no. 04 (December 1999): 225–44. http://dx.doi.org/10.1142/s0218396x99000151.

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Quiet submarine threats and high clutter in the littoral undersea environment increase the processing demands on beamforming arrays, particularly for applications which require in-array autonomous operation. Whereas traditional single-aperture beamforming approaches may falter, the Split-Aperture Conventional Beamforming (SA-CBF) algorithm can be used to meet stringent requirements for more precise bearing estimation. Moreover, by coupling each transducer node with a microprocessor, parallel processing of the split-aperture beamformer on a distributed system can glean advantages in execution speed, fault tolerance, scalability, and cost. In this paper, parallel algorithms for SA-CBF are introduced using coarse-grained and medium-grained forms of decomposition. Performance results from parallel and sequential algorithms are presented using a distributed system testbed comprised of a cluster of workstations connected by a high-speed network. The execution times, parallel efficiencies, and memory requirements of each parallel algorithm are presented and analyzed. The results of these analyses demonstrate that parallel in-array processing holds the potential to meet the needs of future advanced sonar beamforming algorithms in a scalable fashion.

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Mejmaa, Bilal, Chakir Aqil, Ismail Akharraz, and Abdelaziz Ahaitouf. "Implementation of a Reduced Decoding Algorithm Complexity for Quasi-Cyclic Split-Row Threshold Low-Density Parity-Check Decoders." Information 15, no. 11 (November 1, 2024): 684. http://dx.doi.org/10.3390/info15110684.

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We propose two decoding algorithms for quasi-cyclic LDPC codes (QC-LDPC) and implement the more efficient one in this paper. These algorithms depend on the split row for the layered decoding method applied to the Min-Sum (MS) algorithm. We designate the first algorithm “Split-Row Layered Min-Sum” (SRLMS), and the second algorithm “Split-Row Threshold Layered Min-Sum” (SRTLMS). A threshold message passes from one partition to another in SRTLMS, minimizing the gap from the MS and achieving a binary error rate of 3 × 10−5 with Imax = 4 as the maximum number of iterations, resulting in a decrease of 0.25 dB. The simulation’s findings indicate that the SRTLMS is the most efficient variant decoding algorithm for LDPC codes, thanks to its compromise between performance and complexity. This paper presents the two invented algorithms and a comprehensive study of the co-design and implementation of the SRTLMS algorithm. We executed the implementation on a Xilinx Kintex-7 XC7K160 FPGA, achieving a maximum operating frequency of 101 MHz and a throughput of 606 Mbps.

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Lohawech, Panisa, Anchalee Kaewcharoen, and Ali Farajzadeh. "Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces." International Journal of Mathematics and Mathematical Sciences 2021 (June 2, 2021): 1–7. http://dx.doi.org/10.1155/2021/9980309.

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In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.

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YAO, YONGHONG, NASEER SHAHZAD, MIHAI POSTOLACHE, and JEN-CHIH YAO. "Convergence of self-adaptive Tseng-type algorithms for split variational inequalities and fixed point problems." Carpathian Journal of Mathematics 40, no. 3 (April 17, 2024): 753–68. http://dx.doi.org/10.37193/cjm.2024.03.14.

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In this paper, we survey iterative algorithms for solving split variational inequalities and fixed point problems in Hilbert spaces. The investigated split problem is involved in two pseudomonotone operators and two pseudocontractive operators. We propose a self-adaptive Tseng-type algorithm for finding a solution of the split problem. Strong convergence of the suggested algorithm is shown under weaker conditions than sequential weak-to-weak continuity imposed on two pseudomonotone operators.

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Cui, Ying Hua, Yu Ping Zhao, Hui Yang Wang, and Jin He Zhou. "Pre-Split Anti-Collision Binary Tree Algorithm." Applied Mechanics and Materials 220-223 (November 2012): 2403–6. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2403.

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In RFID system, reducing the frequency of collisions is very important for fast tag identification. In this paper, we proposed a pre-split anti-collision algorithm based on binary tree algorithm. The proposed scheme pre-splits the tags into different groups before the reader detects the first tag. Simulation results indicate that the modified algorithm can achieve much better performance than the conventional one.

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Wang, Jian, Sheng Bi, Wenkang Liu, Liping Zhou, Tukun Li, Iain Macleod, and Richard Leach. "Stitching Locally Fitted T-Splines for Fast Fitting of Large-Scale Freeform Point Clouds." Sensors 23, no. 24 (December 14, 2023): 9816. http://dx.doi.org/10.3390/s23249816.

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Parametric splines are popular tools for precision optical metrology of complex freeform surfaces. However, as a promising topologically unconstrained solution, existing T-spline fitting techniques, such as improved global fitting, local fitting, and split-connect algorithms, still suffer the problems of low computational efficiency, especially in the case of large data scales and high accuracy requirements. This paper proposes a speed-improved algorithm for fast, large-scale freeform point cloud fitting by stitching locally fitted T-splines through three steps of localized operations. Experiments show that the proposed algorithm produces a three-to-eightfold efficiency improvement from the global and local fitting algorithms, and a two-to-fourfold improvement from the latest split-connect algorithm, in high-accuracy and large-scale fitting scenarios. A classical Lena image study showed that the algorithm is at least twice as fast as the split-connect algorithm using fewer than 80% control points of the latter.

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Dong, Qiao-Li, and Songnian He. "On Two Projection Algorithms for the Multiple-Sets Split Feasibility Problem." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/347401.

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We present a projection algorithm which modifies the method proposed by Censor and Elfving (1994) and also introduce a self-adaptive algorithm for the multiple-sets split feasibility problem (MSFP). The global rates of convergence are firstly investigated and the sequences generated by two algorithms are proved to converge to a solution of the MSFP. The efficiency of the proposed algorithms is illustrated by some numerical tests.

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BI, GUOAN, A. C. KOT, and ZIHOU MENG. "GENERALISED SPLIT-RADIX ALGORITHMS FOR DFT." Journal of Circuits, Systems and Computers 08, no. 03 (June 1998): 405–9. http://dx.doi.org/10.1142/s0218126698000201.

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This letter presents a general split-radix algorithm based on the decimation-in-time decomposition. It can flexibly compute the discrete Fourier transforms of length-q*2m where q is an odd integer. In comparison with other reported algorithms, our proposed one supports a wider range of sequence lengths, achieves a reduction of arithmetic operations and requires a simple computational structure.

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Ma, Xiaoxuan, and Chao Liu. "Improved Ant Colony Algorithm for the Split Delivery Vehicle Routing Problem." Applied Sciences 14, no. 12 (June 11, 2024): 5090. http://dx.doi.org/10.3390/app14125090.

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The split delivery vehicle routing problem (SDVRP) is a classic combinatorial optimization problem, which is usually solved using a heuristic algorithm. The ant colony optimization algorithm is an excellent heuristic algorithm that has been successfully applied to solve various practical problems, and it has achieved good results. However, in the existing ant colony optimization algorithms, there are issues with weak targeting of different customer selection strategies, difficulty in balancing convergence speed and global search ability, and a predisposition to become trapped in local optima. To solve these problems, this paper proposes an improved ant colony algorithm (IACA). First, in terms of customer point selection, the initial customer and noninitial customer selection strategies are proposed for different customers, and the adaptive selection threshold is designed. Second, in terms of pheromone processing, an initial pheromone distribution method based on a greedy strategy, a pheromone backtracking mechanism, and an adaptive pheromone volatile factor are proposed. Finally, based on the 2-opt local search method, vehicle path self-search and intervehicle path search are proposed to further improve the quality of the solution. This paper tests the performance of the IACA on datasets of different scales. The experimental results show that compared with the clustering algorithm, artificial bee colony algorithm, particle swarm optimization algorithm, traditional ant colony algorithm, and other algorithms, the IACA can achieve more competitive results. Specifically, compared to the path length calculated by other algorithms, the path length calculated by IACA decreased by an average of 1.58%, 4.28%, and 3.64% in small, medium, and large-scale tests, respectively.

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Yu, Youli, Shin Min Kang, and Young Chel Kwun. "Relaxed Extragradient Algorithms for the Split Feasibility Problem." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/468079.

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The purpose of this paper is to introduce a new relaxed extragradient algorithms for the split feasibility problem. Our relaxed extragradient algorithm is new and it generalized some results for solving the split feasibility problem.

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Jambunathan, Suriya Prakash. "A Machine Learning-Based Approach for Antenna Design Using Class_Reg Algorithm Optimized Using Genetic Algorithm." International Journal for Research in Applied Science and Engineering Technology 9, no. 11 (November 30, 2021): 1682–86. http://dx.doi.org/10.22214/ijraset.2021.39097.

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Abstract: Microstrip patch antennas are predominantly in use in mobile communication and healthcare. Their performances are even improved, using Split-Ring Resonator cells. But finding the ideal dimensions of the microstrip patch antenna and calculating the correct number and size of the split ring resonator cells consume a lot of time when we use Electromagnetic Simulation software to design first and then simulate. Using the pre-calculated results of certain sets of microstrip patch antennas with split ring resonators, a machine learning model can be trained and hence be used to predict the antenna metrics when the dimensions are specified. When the machine learning algorithms are combined with feature-optimization algorithms such as the Genetic Algorithm, the efficiency and performance can be improved further. Keywords: Machine Learning, Micro-strip Patch Antenna, Genetic algorithm, Split Ring Resonator.

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Anita Desiani, Annisa Aulia Lestari, and Lucy Chania Agatha. "Analisis Perbandingan Klasifikasi Penyakit Jantung Menggunakan Algoritma Nai ̈ve Bayes dan Algoritma Logistic Regression." Jurnal Rekayasa Elektro Sriwijaya 5, no. 2 (May 19, 2024): 82–90. http://dx.doi.org/10.36706/jres.v5i2.104.

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Heart disease is a condition where parts of the heart are damaged. Thus, early detection is needed. One of them is by doing data mining classification using the Naïve Bayes and Logistic Regression algorithms. This research will compare Naïve Bayes and Logistic Regression algorithms through the training percentage split and k-fold cross validation methods to get the best classification results in detecting heart disease by calculating the average value of precision, recall, and accuracy. The Naïve Bayes algorithm with the training percentage split method produces average values for precision, recall, and accuracy of 83%, 82.5% and 81%, while the Naïve Bayes algorithm with k-fold cross validation provides average values for precision, recall, and accuracy of 83.5%, 85.5% and 83%. Logistic Regression algorithm with percentage split training method produces average values for precision, recall, and accuracy of 73.5%, 73.5% and 73%, while Logistic Regression algorithm using k-fold cross validation produces average values for precision, recall, and accuracy of 84%, 83.5% and 84%. This shows that the Naïve Bayes algorithm using percentage split is better than Logistic Regression, but when using the k-fold cross validation method, the Logistic Regression algorithm has a significant increase compared to Naïve Bayes. So that to classify heart disease is better with the Logistic Regression Algorithm with the k-fold cross validation method.

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28

Al-Nsour, Esam, Azzam Sleit, and Mohammad Alshraideh. "SOLD: A node-Splitting algorithm for R-tree based on Objects’ Locations Distribution." Journal of Information Science 45, no. 2 (July 3, 2018): 169–95. http://dx.doi.org/10.1177/0165551518785561.

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Spatial data indexing methods are of extreme importance as they massively build up as a result of the explosive growth in capturing data with spatial features. No matter how much the data size is, eventually it will reside on disk pages. Disk pages have to be properly indexed to preserve spatial properties of objects, optimise disk space usage and improve objects’ retrieval performance. One of the most popular spatial data indexes is the R-tree which is a height balanced tree data structure, where leaf nodes resemble disk pages and contain pointers to objects’ locations. A single tree node can host up to a maximum number of objects, where any more insertion makes it an overflown node and it has to be split. Better splits lead to better index performance and more utilisation of disk space. In this work, we introduce a new way of finding the most proper split for an overflown node in the R-tree index. The proposed work scans – in a linear cost – the overflown node’s objects once to identify the distribution of objects’ locations (minimum bounding rectangles (MBRs)) in relative to its node’s bounding rectangle (node’s MBR). It uses objects’ locations to calculate – for each main axis – the split quality factors: expected overlap between resulting nodes, objects distribution evenness among resulting nodes and the perimeter of resulting nodes. The axis with better combined quality factors values is selected as the split axis. The Splitting based on Objects’ Locations Distribution (SOLD) algorithm was implemented and tested against two other splitting algorithms, experiments using synthetic and real data files showed good results and it outperformed both algorithms in index creation tests and data retrieval tests.

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29

Li, Xiaochun, Xiaoxiao Liu, and Fugen Gao. "The Ball-Relaxed Gradient-Projection Algorithm for Split Feasibility Problem." Journal of Function Spaces 2022 (April 12, 2022): 1–6. http://dx.doi.org/10.1155/2022/9991466.

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In this paper, we concern with the split feasibility problem (SFP) whenever the convex sets involved are composed of level sets. By applying Gradient-projection algorithm which is used to solve constrained convex minimization problem of a real valued convex function, we construct two new algorithms for the split feasibility problem and prove that both of them are convergent weakly to a solution of the feasibility problem. In the end, as an application, we obtain a new algorithm for solving the split equality problem.

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30

Jia, Huijuan, Shufen Liu, and Yazheng Dang. "An Inertial Accelerated Algorithm for Solving Split Feasibility Problem with Multiple Output Sets." Journal of Mathematics 2021 (November 5, 2021): 1–12. http://dx.doi.org/10.1155/2021/6252984.

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The paper proposes an inertial accelerated algorithm for solving split feasibility problem with multiple output sets. To improve the feasibility, the algorithm involves computing of projections onto relaxed sets (half spaces) instead of computing onto the closed convex sets, and it does not require calculating matrix inverse. To accelerate the convergence, the algorithm adopts self-adaptive rules and incorporates inertial technique. The strong convergence is shown under some suitable conditions. In addition, some newly derived results are presented for solving the split feasibility problem and split feasibility problem with multiple output sets. Finally, numerical experiments illustrate that the algorithm converges more quickly than some existing algorithms. Our results extend and improve some methods in the literature.

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31

Dong, Qiao-Li, and Songnian He. "Modified Projection Algorithms for Solving the Split Equality Problems." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/328787.

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Анотація:

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.

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32

Tang, Yu-Chao, Ji-Gen Peng, and Li-Wei Liu. "A CYCLIC ALGORITHM FOR THE SPLIT COMMON FIXED POINT PROBLEM OF DEMICONTRACTIVE MAPPINGS IN HILBERT SPACES." Mathematical Modelling and Analysis 17, no. 4 (September 1, 2012): 457–66. http://dx.doi.org/10.3846/13926292.2012.706236.

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The split common fixed point problem has been investigated recently, which is a generalization of the split feasibility problem and of the convex feasibility problem. We construct a cyclic algorithm to approximate a solution of the split common fixed point problem for the demicontractive mappings in a Hilbert space. Our results improve and extend previously discussed related problems and algorithms.

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33

Hermansyah, Mas'ud. "ANALISIS SENTIMEN TWITTER UNTUK MENGETAHUI KESAN MASYARAKAT TENTANG PELAKSANAAN POMPROV JAWA TIMUR TAHUN 2022 DENGAN PERBANDINGAN METODE NAÏVE BAYES CLASSIFIER DAN DECISION TREE BERBASIS SMOTE." Jurnal Informatika Dan Tekonologi Komputer (JITEK) 2, no. 3 (November 29, 2022): 249–55. http://dx.doi.org/10.55606/jitek.v2i3.551.

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Sentiment analysis is a method used to understand, extract, and automatically process text data to get the sentiment contained in an opinion. Sentiment analysis will be used to process comments made by the community or supporters of each participant of POMPROV East Java 2022 through various media, including Twitter, regarding the progress or results of POMPROV East Java 2022. The number of comments, the authors use data mining methods and algorithms to process the comment data to get information about the POMPROV East Java 2022 event. The Naïve Bayes Classifier and Decision Tree classification algorithms are used as tools to classify comments expressed by users. Based on the results of experiments that have been carried out four times according to the number of data splits and twice based on the algorithm used, it can be concluded that the use of the SMOTE algorithm can increase the accuracy of the various data split compositions used. The best results of the Naïve Bayes Classifier method are found in the 7:3 data distribution which increases the accuracy by 14.52% and the Decision Tree method in the 9:1 data division increases the accuracy by 9.45%.

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34

Che Rose, Farid Zamani, Mohd Tahir Ismail, and Mohd Hanafi Tumin. "Outliers detection in state-space model using indicator saturation approach." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 3 (June 1, 2021): 1688. http://dx.doi.org/10.11591/ijeecs.v22.i3.pp1688-1696.

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Structural changes that occur due to outliers may reduce the accuracy of an estimated time series model, shifting the mean distribution and causing forecast failure. This study used general-to-specific approach to detect outliers via indicator saturation approach in the local level model framework. Focusing on impulse indicator saturation, performance recorded by the suggested approach was evaluated using Monte Carlo simulations. To tackle the issue of higher number of regressors compared to the number of observations, this research utilized the split-half approach algorithm. We found that the impulse indicator saturation performance relies heavily on the size of outlier, location of outlier and number of splits in the series examined. Detection of outliers using sequential and non-sequential algorithms is the most crucial issue in this study. The sequential searching algorithm was able to outperform the non-sequential searching algorithm in eliminating the non-significant indicators based on potency and gauge. The outliers captured using impulse indicator saturation in financial times stock exchange (FTSE) United States of America (USA) shariah index correspond to the financial crisis in 2008-2009.

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35

Rajappa, Gautham Puttur, Joseph H. Wilck, and John E. Bell. "An Ant Colony Optimization and Hybrid Metaheuristics Algorithm to Solve the Split Delivery Vehicle Routing Problem." International Journal of Applied Industrial Engineering 3, no. 1 (January 2016): 55–73. http://dx.doi.org/10.4018/ijaie.2016010104.

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Split Delivery Vehicle Routing Problem (SDVRP) is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) that allows the same customer to be served by more than one vehicle. Existing literature has applied Ant Colony Optimization (ACO) and Genetic Algorithm (GA) to other variants of VRP but no known research effort has applied ACO or a combination of ACO and GA to solve the Split Delivery Vehicle Routing Problem (SDVRP). Hence, two algorithms using ACO and hybrid metaheuristics algorithm comprising a combination of ACO, Genetic Algorithm (GA) and heuristics is proposed and tested on existing benchmark SDVRP problems. The results indicate that the two proposed algorithms are competitive in both solution quality and solution time and for some problem instances, the best ever solutions have been found.

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36

Dang, Ya-zheng, Long Wang, and Yao-heng Yang. "New hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem." Applied Mathematics-A Journal of Chinese Universities 38, no. 1 (March 2023): 144–58. http://dx.doi.org/10.1007/s11766-023-4464-7.

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AbstractIn this paper, we propose two hybrid inertial CQ projection algorithms with line-search process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.

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37

GARCÍA, PEDRO, DAMIÁN LÓPEZ, and MANUEL VÁZQUEZ DE PARGA. "EFFICIENT DETERMINISTIC FINITE AUTOMATA SPLIT-MINIMIZATION DERIVED FROM BRZOZOWSKI'S ALGORITHM." International Journal of Foundations of Computer Science 25, no. 06 (September 2014): 679–96. http://dx.doi.org/10.1142/s0129054114500282.

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Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft's classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.

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38

Ramdhani, Yudi, Cakra Mahendra Putra, and Doni Purnama Alamsyah. "Heart failure prediction based on random forest algorithm using genetic algorithm for feature selectio." International Journal of Reconfigurable and Embedded Systems (IJRES) 12, no. 2 (July 1, 2023): 205. http://dx.doi.org/10.11591/ijres.v12.i2.pp205-214.

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A disorder or illness called heart failure results in the heart becoming weak or damaged. In order to avoid heart failure early on, it is crucial to understand the causes of heart failure. Based on validation, two experimental processing steps will be applied to the dataset of clinical records related to heart failure. Testing will be done in the first step utilizing six different classification algorithms, including K-nearest neighbor, neural network, random forest, decision tree, Naïve Bayes, and support vector machine (SVM). Cross-validation was employed to conduct the test. According to the results, the random forest algorithm performed better than the other five algorithms in tests employing the algorithm. Subsequent testing uses an algorithm with the best accuracy value, which will then be tested again using split validation with varying split ratios and genetic algorithms as a selection feature. The value generated from testing using the genetic algorithm selection feature is better than the random forest algorithm alone, which is recorded to produce an accuracy value of 93.36% in predicting the survival of heart failure patients.

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39

Meng, Xiangchen, Jie Cheng, Shaohua Zhao, Sihan Liu, and Yunjun Yao. "Estimating Land Surface Temperature from Landsat-8 Data using the NOAA JPSS Enterprise Algorithm." Remote Sensing 11, no. 2 (January 15, 2019): 155. http://dx.doi.org/10.3390/rs11020155.

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Land surface temperature (LST) is one of the key parameters in hydrology, meteorology, and the surface energy balance. The National Oceanic and Atmospheric Administration (NOAA) Joint Polar Satellite System (JPSS) Enterprise algorithm is adapted to Landsat-8 data to obtain the estimate of LST. The coefficients of the Enterprise algorithm were obtained by linear regression using the analog data produced by comprehensive radiative transfer modeling. The performance of the Enterprise algorithm was first tested by simulation data and then validated by ground measurements. In addition, the accuracy of the Enterprise algorithm was compared to the generalized split-window algorithm and the split-window algorithm of Sobrino et al. (1996). The validation results indicate the Enterprise algorithm has a comparable accuracy to the other two split-window algorithms. The biases (root mean square errors) of the Enterprise algorithm were 1.38 (3.22), 1.01 (2.32), 1.99 (3.49), 2.53 (3.46), and −0.15 K (1.11 K) at the SURFRAD, HiWATER_A, HiWATER_B, HiWATER_C sites and BanGe site, respectively, whereas those values were 1.39 (3.20), 1.0 (2.30), 1.93 (3.48), 2.53 (3.35), and −0.35 K (1.16 K) for the generalized split-window algorithm, 1.45 (3.39), 1.08 (2.41), 2.16 (3.67), 2.52 (3.58), and 0.02 K (1.12 K) for the split-window algorithm of Sobrino, respectively. This study provides an alternative method to estimate LST from Landsat-8 data.

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40

Wu, Dingping, and Mihai Postolache. "Two iterative algorithms for solving the split common fixed point problems." Filomat 34, no. 13 (2020): 4375–86. http://dx.doi.org/10.2298/fil2013375w.

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The purpose of this paper is to study the split common fixed point problems (SCFP) involved in nonexpansive mappings in real Hilbert space. We introduce two iterative algorithms for finding a solution of the SCFP involved in nonexpansive mappings, where one is a Mann-type iterative algorithm and another is a Halpern-type iterative algorithm.

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41

Sharma, Dr Nirmla, and Sameera Iqbal Muhmmad Iqbal. "Applying Decision Tree Algorithm Classification and Regression Tree (CART) Algorithm to Gini Techniques Binary Splits." International Journal of Engineering and Advanced Technology 12, no. 5 (June 30, 2023): 77–81. http://dx.doi.org/10.35940/ijeat.e4195.0612523.

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Decision tree study is a predictive modelling tool that is used over many grounds. It is constructed through an algorithmic technique that is divided the dataset in different methods created on varied conditions. Decisions trees are the extreme dominant algorithms that drop under the set of supervised algorithms. However, Decision Trees appearance modest and natural, there is nothing identical modest near how the algorithm drives nearby the procedure determining on splits and how tree snipping happens. The initial object to appreciate in Decision Trees is that it splits the analyst field, i.e., the objective parameter into diverse subsets which are comparatively more similar from the viewpoint of the objective parameter. Gini index is the name of the level task that has applied to assess the binary changes in the dataset and worked with the definite object variable “Success” or “Failure”. Split creation is basically covering the dataset values. Decision trees monitor a top-down, greedy method that has recognized as recursive binary splitting. It has statistics for 15 statistics facts of scholar statistics on pass or fails an online Machine Learning exam. Decision trees are in the class of supervised machine learning. It has been commonly applied as it has informal implement, interpreted certainly, derived to quantitative, qualitative, nonstop, and binary splits, and provided consistent outcomes. The CART tree has regression technique applied to expected standards of nonstop variables. CART regression trees are an actual informal technique of understanding outcomes.

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42

Ofem, Austine Efut, Unwana Effiong Udofia, and Donatus Ikechi Igbokwe. "New Iterative Algorithm for Solving Constrained Convex Minimization Problem and Split Feasibility Problem." European Journal of Mathematical Analysis 1, no. 2 (October 1, 2021): 106–32. http://dx.doi.org/10.28924/ada/ma.1.106.

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The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Also, we show that our proposed iterative algorithm converges weakly and strongly to the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Furthermore, it is proved analytically that our new iterative algorithm converges faster than one of the leading iterative algorithms in the literature for almost contraction mappings. Some numerical examples are also provided and used to show that our new iterative algorithm has better rate of convergence than all of S, Picard-S, Thakur and M iterative algorithms for almost contraction mappings and generalized α-nonexpansive mappings. Again, we show that the proposed iterative algorithm is stable with respect to T and data dependent for almost contraction mappings. Some applications of our main results and new iterative algorithm are considered. The results in this article are improvements, generalizations and extensions of several relevant results existing in the literature.

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43

HorvÃ¡tha, I. "Stochastic Split Determinant Algorithms." Nuclear Physics B - Proceedings Supplements 83-84, no. 1-3 (March 2000): 804–6. http://dx.doi.org/10.1016/s0920-5632(00)00425-4.

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44

Horváth, Ivan. "Stochastic split determinant algorithms." Nuclear Physics B - Proceedings Supplements 83-84 (April 2000): 804–6. http://dx.doi.org/10.1016/s0920-5632(00)91809-7.

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45

Dang, Yazheng, and Yan Gao. "Inertial Iteration for Split Common Fixed-Point Problem for Quasi-Nonexpansive Operators." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/386930.

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Анотація:

Inspired by the note on split common fixed-point problem for quasi-nonexpansive operators presented by Moudafi (2011), based on the very recent work by Dang et al. (2012), in this paper, we propose an inertial iterative algorithm for solving the split common fixed-point problem for quasi-nonexpansive operators in the Hilbert space. We also prove the asymptotical convergence of the algorithm under some suitable conditions. The results improve and develop previously discussed feasibility problems and related algorithms.

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46

Wang, Lijuan, Ni Guo, Wei Wang, and Hongchao Zuo. "Optimization of the Local Split-Window Algorithm for FY-4A Land Surface Temperature Retrieval." Remote Sensing 11, no. 17 (August 27, 2019): 2016. http://dx.doi.org/10.3390/rs11172016.

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FY-4A is a second generation of geostationary orbiting meteorological satellite, and the successful launch of FY-4A satellite provides a new opportunity to obtain diurnal variation of land surface temperature (LST). In this paper, different underlying surfaces-observed data were applied to evaluate the applicability of the local split-window algorithm for FY-4A, and the local split-window algorithm parameters were optimized by the artificial intelligent particle swarm optimization (PSO) algorithm to improve the accuracy of retrieved LST. Results show that the retrieved LST can efficiently reproduce the diurnal variation characteristics of LST. However, the estimated values deviate hugely from the observed values when the local split-window algorithms are directly used to process the FY-4A satellite data, and the root mean square errors (RMSEs) are approximately 6K. The accuracy of the retrieved LST cannot be effectively improved by merely modifying the emissivity-estimated model or optimizing the algorithm. Based on the measured emissivity, the RMSE of LST retrieved by the optimized local split-window algorithm is reduced to 3.45 K. The local split-window algorithm is a simple and easy retrieval approach that can quickly retrieve LST on a regional scale and promote the application of FY-4A satellite data in related fields.

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47

ADAMU, ABUBAKAR, and AISHA A. ADAM. "Approximation of solutions of split equality fixed point problems with applications." Carpathian Journal of Mathematics 37, no. 3 (July 15, 2021): 381–92. http://dx.doi.org/10.37193/cjm.2021.03.02.

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In this paper, we introduce and study an inertial algorithm for approximating solutions of split equality fixed point problem (SEFPP), involving quasi-phi-nonexpansive mappings in uniformly smooth and 2-uniformly convex real Banach spaces and establish a strong convergence theorem. We give applications of our result to split equality problem (SEP), split equality variational inclusion problem (SEVIP) and split equality equilibrium problem (SEEP). Our results extend, generalize and unify several recent inertial-type algorithms for approximating solutions of SEP and SEVIP. Moreover, to the best of our knowledge, our propose method which does not require any compactness type assumption on the operators is the first inertial algorithm for approximating solutions of SEFPP, SEP, SEVIP and SEEP in Banach spaces.

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48

Nandal, Ashish, Renu Chugh, and Mihai Postolache. "Iteration Process for Fixed Point Problems and Zeros of Maximal Monotone Operators." Symmetry 11, no. 5 (May 10, 2019): 655. http://dx.doi.org/10.3390/sym11050655.

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We introduce an iterative algorithm which converges strongly to a common element of fixed point sets of nonexpansive mappings and sets of zeros of maximal monotone mappings. Our iterative method is quite general and includes a large number of iterative methods considered in recent literature as special cases. In particular, we apply our algorithm to solve a general system of variational inequalities, convex feasibility problem, zero point problem of inverse strongly monotone and maximal monotone mappings, split common null point problem, split feasibility problem, split monotone variational inclusion problem and split variational inequality problem. Under relaxed conditions on the parameters, we derive some algorithms and strong convergence results to solve these problems. Our results improve and generalize several known results in the recent literature.

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49

Delsarte, P., and Y. Genin. "The split Levinson algorithm." IEEE Transactions on Acoustics, Speech, and Signal Processing 34, no. 3 (June 1986): 470–78. http://dx.doi.org/10.1109/tassp.1986.1164830.

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50

Meyer, Ulrich, Hung Tran, and Konstantinos Tsakalidis. "Certifying Induced Subgraphs in Large Graphs." Journal of Graph Algorithms and Applications 28, no. 3 (September 10, 2024): 49–68. http://dx.doi.org/10.7155/jgaa.v28i3.2971.

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Анотація:

We introduce I/O-efficient certifying algorithms for the recognition of bipartite, split, threshold, bipartite chain, and trivially perfect graphs. When the input graph is a member of the respective class, the certifying algorithm returns a certificate that characterizes this class.Otherwise, it returns a forbidden induced subgraph as a certificate for non-membership.On a graph with $n$ vertices and $m$ edges, our algorithms take $\mathcal O(\text{sort}(n + m))$ I/Os in the worst case for split, threshold and trivially perfect graphs.In the same complexity bipartite and bipartite chain graphs can be certified with high probability.We provide implementations and an experimental evaluation for split and threshold graphs.

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