Journal articles: 'Nonlinear projection'

1

Dudek, Ewa, and Konstanty Holly. "Nonlinear orthogonal projection." Annales Polonici Mathematici 59, no. 1 (1994): 1–31. http://dx.doi.org/10.4064/ap-59-1-1-31.

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2

Ashlock, Daniel, and Andrew McEachern. "Evolutionary Nonlinear Projection." IEEE Transactions on Evolutionary Computation 19, no. 6 (December 2015): 857–69. http://dx.doi.org/10.1109/tevc.2015.2395091.

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3

Jing, Xiao Yuan, Min Li, Yong Fang Yao, Song Hao Zhu, and Sheng Li. "A New Kernel Orthogonal Projection Analysis Approach for Face Recognition." Advanced Materials Research 760-762 (September 2013): 1627–32. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.1627.

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In the field of face recognition, how to extract effective nonlinear discriminative features is an important research topic. In this paper, we propose a new kernel orthogonal projection analysis approach. We obtain the optimal nonlinear projective vector which can differentiate one class and its adjacent classes, by using the Fisher criterion and constructing the specific between-class and within-class scatter matrices in kernel space. In addition, to eliminate the redundancy among projective vectors, our approach makes every projective vector satisfy locally orthogonal constraints by using the corresponding class and part of its most adjacent classes. Experimental results on the public AR and CAS-PEAL face databases demonstrate that the proposed approach outperforms several representative nonlinear projection analysis methods.

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4

Masry, Elias, and Dag Tjøstheim. "Additive Nonlinear ARX Time Series and Projection Estimates." Econometric Theory 13, no. 2 (April 1997): 214–52. http://dx.doi.org/10.1017/s0266466600005739.

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We propose projections as means of identifying and estimating the components (endogenous and exogenous) of an additive nonlinear ARX model. The estimates are nonparametric in nature and involve averaging of kernel-type estimates. Such estimates have recently been treated informally in a univariate time series situation. Here we extend the scope to nonlinear ARX models and present a rigorous theory, including the derivation of asymptotic normality for the projection estimates under a precise set of regularity conditions.

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5

Atkinson, Kendall E., and Florian A. Potra. "Projection and Iterated Projection Methods for Nonlinear Integral equations." SIAM Journal on Numerical Analysis 24, no. 6 (December 1987): 1352–73. http://dx.doi.org/10.1137/0724087.

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6

Yuen, P. C., G. C. Feng, and Y. Y. Tang. "Printed Chinese Character Similarity Measurement Using Ring Projection and Distance Transform." International Journal of Pattern Recognition and Artificial Intelligence 12, no. 02 (March 1998): 209–21. http://dx.doi.org/10.1142/s0218001498000142.

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This paper presents a new Chinese character similarity measurement method based on the ring projection algorithm and distance transform. The ring projection algorithm is used to transform a character image with two independent variables into a function of one independent variable in the ring projection space. This representation of character in the ring projection space has been proved to be in orientation and scale invariant. However, this representation will be distorted nonlinearly in the presence of noise. Therefore, common linear metrics such as Euclidean distance, cannot be applied to measure distance. To solve the nonlinear distortion problem, distance transform is proposed as a nonlinear metric. The similarity measurement is performed using the distance transformed image in the ring projection space. A number of Chinese characters are selected to evaluate the capability of the proposed measurement scheme and the results are encouraging.

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7

Breaban, Mihaela, and Henri Luchian. "Outlier Detection with Nonlinear Projection Pursuit." International Journal of Computers Communications & Control 8, no. 1 (November 13, 2012): 30. http://dx.doi.org/10.15837/ijccc.2013.1.165.

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8

Agarwal, Ravi P., Yeol Je Cho, and Xiaolong Qin. "Generalized Projection Algorithms for Nonlinear Operators." Numerical Functional Analysis and Optimization 28, no. 11-12 (December 10, 2007): 1197–215. http://dx.doi.org/10.1080/01630560701766627.

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9

Cai, Zongwu, and Elias Masry. "NONPARAMETRIC ESTIMATION OF ADDITIVE NONLINEAR ARX TIME SERIES: LOCAL LINEAR FITTING AND PROJECTIONS." Econometric Theory 16, no. 4 (August 2000): 465–501. http://dx.doi.org/10.1017/s0266466600164011.

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We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ a local polynomial fitting scheme coupled with projections. We establish the weak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given.

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10

Gu, Guang Hui, and Yong Fu Su. "Generalized System for Relaxed Cocoercive and Involving Projective Nonexpansive Mapping Variational Inequalities." Advanced Materials Research 393-395 (November 2011): 792–95. http://dx.doi.org/10.4028/www.scientific.net/amr.393-395.792.

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Firstly, the concept of projective nonexpansive mappings is presented in this paper. The approximate solvability of a generalized system for relaxed cocoercive and involving projective nonexpansive mapping nonlinear variational inequalities in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of many authors.

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11

Lee, Sang-Ho, and Ted Belytschko. "H-Adaptive Methods for Nonlinear Dynamic Analysis of Shell Structures." Shock and Vibration 2, no. 3 (1995): 193–204. http://dx.doi.org/10.1155/1995/489694.

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The implementation and application of h-adaptivity in an explicit finite element program for nonlinear structural dynamics is described. Particular emphasis is placed on developing procedures for general purpose structural dynamics programs and efficiently handling adaptivity in shell elements. New projection techniques for error estimation and projecting variables on new meshes after fission or fusion are described. Several problems of severe impact are described.

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12

Grammont, Laurence, Rekha P. Kulkarni, and Paulo B. Vasconcelos. "Modified projection and the iterated modified projection methods for nonlinear integral equations." Journal of Integral Equations and Applications 25, no. 4 (December 2013): 481–516. http://dx.doi.org/10.1216/jie-2013-25-4-481.

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13

Dellwo, David R., and Morton B. Friedman. "Accelerated Projection and Iterated Projection Methods with Applications to Nonlinear Integral Equations." SIAM Journal on Numerical Analysis 28, no. 1 (February 1991): 236–50. http://dx.doi.org/10.1137/0728013.

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14

Beard, Randal, John Kenney, Jacob Gunther, Jonathan Lawton, and Wynn Stirling. "Nonlinear Projection Filter Based on Galerkin Approximation." Journal of Guidance, Control, and Dynamics 22, no. 2 (March 1999): 258–66. http://dx.doi.org/10.2514/2.4403.

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15

Yonggao Yang, J. X. Chen, Woosung Kim, and Changjin Kee. "Nonlinear projection: using deformations in 3D viewing." Computing in Science & Engineering 5, no. 2 (March 2003): 54–59. http://dx.doi.org/10.1109/mcise.2003.1182962.

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16

O’Leary, Dianne P., and Bert W. Rust. "Variable projection for nonlinear least squares problems." Computational Optimization and Applications 54, no. 3 (August 2, 2012): 579–93. http://dx.doi.org/10.1007/s10589-012-9492-9.

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17

Li, Li, and Thomas Kunz. "Cooperative node localization using nonlinear data projection." ACM Transactions on Sensor Networks 5, no. 1 (February 2009): 1–26. http://dx.doi.org/10.1145/1464420.1464421.

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18

Rodriguez, Jesús, and Daniel Sweet. "Projection methods for nonlinear boundary value problems." Journal of Differential Equations 58, no. 2 (June 1985): 282–93. http://dx.doi.org/10.1016/0022-0396(85)90017-8.

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19

Voss, Heinrich. "Iterative Projection Methods for Sparse Nonlinear Eigenproblems." PAMM 4, no. 1 (December 2004): 722–25. http://dx.doi.org/10.1002/pamm.200410342.

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20

Giselsson, Pontus. "Nonlinear Forward-Backward Splitting with Projection Correction." SIAM Journal on Optimization 31, no. 3 (January 2021): 2199–226. http://dx.doi.org/10.1137/20m1345062.

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21

Dang, Yazheng, and Wenwen Liu. "A Nonmonotone Projection Method for Constrained System of Nonlinear Equations." Mathematical Problems in Engineering 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/8270649.

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This paper deals with the nonmonotone projection algorithm for constrained nonlinear equations. For some starting points, the previous projection algorithms for the problem may encounter slow convergence which is related to the monotone behavior of the iterative sequence as well as the iterative direction. To circumvent this situation, we adopt the nonmonotone technique introduced by Dang to develop a nonmonotone projection algorithm. After constructing the nonmonotone projection algorithm, we show its convergence under some suitable condition. Preliminary numerical experiment is reported at the end of this paper, from which we can see that the algorithm we propose converges more quickly than that of the usual projection algorithm for some starting points.

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22

Chen, Lijuan, Zihao Zhang, Yapeng Zhang, Xiaoshuang Xiong, Fei Fan, and Shuangbao Ma. "Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation." Symmetry 13, no. 9 (September 16, 2021): 1715. http://dx.doi.org/10.3390/sym13091715.

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For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

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23

Kulkarni, Rekha P., and T. J. Nidhin. "Asymptotic error analysis of projection and modified projection methods for nonlinear integral equations." Journal of Integral Equations and Applications 27, no. 1 (March 2015): 67–101. http://dx.doi.org/10.1216/jie-2015-27-1-67.

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24

Nahid, Nilofar, Payel Das, and Gnaneshwar Nelakanti. "Projection and multi projection methods for nonlinear integral equations on the half-line." Journal of Computational and Applied Mathematics 359 (October 2019): 119–44. http://dx.doi.org/10.1016/j.cam.2019.03.042.

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25

Kimura, Masashi, Yusaku Yamaguchi, Omar M. Abou Al-Ola, and Tetsuya Yoshinaga. "Tomographic Inverse Problem with Estimating Missing Projections." Mathematical Problems in Engineering 2019 (March 13, 2019): 1–11. http://dx.doi.org/10.1155/2019/7932318.

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Image reconstruction in computed tomography can be treated as an inverse problem, namely, obtaining pixel values of a tomographic image from measured projections. However, a seriously degraded image with artifacts is produced when a certain part of the projections is inaccurate or missing. A novel method for simultaneously obtaining a reconstructed image and an estimated projection by solving an initial-value problem of differential equations is proposed. A system of differential equations is constructed on the basis of optimizing a cost function of unknown variables for an image and a projection. Three systems described by nonlinear differential equations are constructed, and the stability of a set of equilibria corresponding to an optimized solution for each system is proved by using the Lyapunov stability theorem. To validate the theoretical result given by the proposed method, metal artifact reduction was numerically performed.

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26

Białoń, Paweł. "Large-scale nonlinear programming algorithm using projection methods." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 20, no. 2 (2000): 171. http://dx.doi.org/10.7151/dmdico.1011.

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27

Johnson, Michael T., and Richard J. Povinelli. "Generalized phase space projection for nonlinear noise reduction." Physica D: Nonlinear Phenomena 201, no. 3-4 (February 2005): 306–17. http://dx.doi.org/10.1016/j.physd.2005.01.011.

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28

Kewitsch, Anthony S., and Amnon Yariv. "Nonlinear optical properties of photoresists for projection lithography." Applied Physics Letters 68, no. 4 (January 22, 1996): 455–57. http://dx.doi.org/10.1063/1.116411.

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29

Degenhard, Andreas, and Javier Rodríguez-Laguna. "Construction of Projection Operators for Nonlinear Evolutionary Dynamics." Multiscale Modeling & Simulation 4, no. 2 (January 2005): 641–63. http://dx.doi.org/10.1137/040603152.

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30

Grohs, Philipp, Hanne Hardering, Oliver Sander, and Markus Sprecher. "Projection-Based Finite Elements for Nonlinear Function Spaces." SIAM Journal on Numerical Analysis 57, no. 1 (January 2019): 404–28. http://dx.doi.org/10.1137/18m1176798.

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31

Chelidze, David. "Smooth local subspace projection for nonlinear noise reduction." Chaos: An Interdisciplinary Journal of Nonlinear Science 24, no. 1 (March 2014): 013121. http://dx.doi.org/10.1063/1.4865754.

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32

Berthon, Christophe, and Didier Reignier. "Nonlinear projection methods to approximate combustion turbulent flows." Computers & Fluids 33, no. 5-6 (June 2004): 679–85. http://dx.doi.org/10.1016/j.compfluid.2003.02.001.

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33

Parker, D. F., A. P. Mayer, and A. A. Maradudin. "The projection method for nonlinear surface acoustic waves." Wave Motion 16, no. 2 (September 1992): 151–62. http://dx.doi.org/10.1016/0165-2125(92)90039-5.

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34

She-feng, Zhao, and Fei Pu-sheng. "Projection and contraction methods for nonlinear complementarity problem." Wuhan University Journal of Natural Sciences 5, no. 4 (December 2000): 391–96. http://dx.doi.org/10.1007/bf02850762.

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35

Xie, Xuping, Guannan Zhang, and Clayton G. Webster. "Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network." Mathematics 7, no. 8 (August 19, 2019): 757. http://dx.doi.org/10.3390/math7080757.

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In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the method optimally approximates the full order model in the low-dimensional space with a given supervised learning task. Moreover, our approach is non-intrusive, such that it can be applied to other complex nonlinear dynamical systems with sophisticated legacy codes. We demonstrate the performance of our method through the numerical simulation of a two-dimensional flow past a circular cylinder with Reynolds number Re = 100. The results reveal that the new data-driven model is significantly more accurate than standard projection-based approaches.

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36

Qin, Xiaolong, Tianze Wang, and Sun Young Cho. "Hybrid Projection Algorithms for Asymptotically Strict Quasi-ϕ-Pseudocontractions." Abstract and Applied Analysis 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/142626.

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37

Chen, Jiun-Shyan, and Chunhui Pan. "A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part I: Theory." Journal of Applied Mechanics 63, no. 4 (December 1, 1996): 862–68. http://dx.doi.org/10.1115/1.2787240.

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A least-squares-based pressure projection method is proposed for the nonlinear analysis of nearly incompressible hyperelastic materials. The strain energy density function is separated into distortional and dilatational parts by the use of Penn’s invariants such that the hydrostatic pressure is solely determined from the dilatational strain energy density. The hydrostatic pressure and hydrostatic pressure increment calculated from displacements are projected onto appropriate pressure fields through the least-squares method. The method is applicable to lower and higher order elements and the projection procedures can be implemented into the displacement based nonlinear finite element program. By the use of certain pressure interpolation functions and reduced integration rules in the pressure projection equations, this method can be degenerated to a nonlinear version of the selective reduced integration method.

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38

Kim, Kyung. "System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space." Mathematics 6, no. 10 (October 11, 2018): 198. http://dx.doi.org/10.3390/math6100198.

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In this manuscript, we study a system of extended general variational inequalities (SEGVI) with several nonlinear operators, more precisely, six relaxed ( α , r ) -cocoercive mappings. Using the projection method, we show that a system of extended general variational inequalities is equivalent to the nonlinear projection equations. This alternative equivalent problem is used to consider the existence and convergence (or approximate solvability) of a solution of a system of extended general variational inequalities under suitable conditions.

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39

Ledermann, Florian. "Classifying Cartographic Projections Based on Dynamic Analysis of Program Code." Abstracts of the ICA 2 (October 9, 2020): 1. http://dx.doi.org/10.5194/ica-abs-2-38-2020.

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Abstract. Analyzing a given map to identify its projection and other geometrical properties has long been an important aspect of cartographic analysis. If explicit information about the projection used in a particular map is not available, the properties of the cartographic transformation can sometimes be reconstructed from the map image. However, such a process of projection analysis requires significant manual labor and oversight.For digital maps, we usually expect the projection from geographic space to map space to have been calculated by a computer program. Such a program can be expected to contain the implementation of the mathematical rules of the projection and subsequent coordinate transformations such as translation and scaling. The program code, therefore, contains information that would allow an analyst to reliably identify map projections and other geometrical transformations applied to the input data.In the case of interactive online maps, the code generating the map is in fact delivered to the map user and could be used for cartographic analysis. The core idea of our novel method proposed for map analysis is to apply reverse engineering techniques on the code implementing the cartographic transformations in order to retrieve the properties of the applied map projection. However, automatic reasoning about computer code by way of static analysis (analyzing the source code without running it) is provably limited – for example, the code delivered to the map user may contain a whole library of different map projections, of which only a specific one may be actually used at runtime. Instead, we propose a dynamic analysis approach to observe and monitor the operations performed by the code as the program runs, and to retrieve the mathematical operations that have been used to calculate the coordinates of every graphical element on the map.The presented method produces, for every graphical element of the map, a transformation graph consisting of low-level mathematical operations. Cartographic projections can be identified as distinctive patterns in the transformation graph, and can be distinguished in a fully automatic way by matching a set of predefined patterns against a particular graph.Projections vary widely in their arithmetic structure, and therefore by the structure of the corresponding transformation graphs extracted from program code. Some projections can be computed directly using continuous equations involving trigonometric functions. Other projections involve solving nonlinear equations, which need to be solved by approximation. Composite projections use different projections depending on some threshold value. Yet other projections, such as the Robinson projection, define a table of predefined values, between which interpolation is used etc.. In each of these cases, we expect to find the operations corresponding to the mathematical structure of the projection in the transformation graph extracted by the presented method.For verifying the method, we have implemented the patterns of several well-known cartographic projections based on the literature and have used it on the transformation graphs extracted from a variety of sample programs. To ensure a diversity of implementations, we have evaluated programs using different and independent JavaScript implementations of projections, including the open source libraries D3.js, proj4js, Leaflet, OpenLayers, and informal implementations of example programs found online. For these case studies, we could successfully identify many projections based on identifying patterns in the transformation graph in a fully automated, unsupervised manner.In the future, the proposed method may be further developed for many innovative application scenarios, such as building a “cartographic search engine” or constructing novel tools for semi-automatic cartographic analysis and review.

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40

Shuvalova, L. E. "Projection solution methods for one nonlinear singular integral equation." Russian Mathematics 52, no. 10 (October 2008): 67–71. http://dx.doi.org/10.3103/s1066369x08100101.

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41

Ono, Naoki, and Kiichi Urahama. "Monochromatic Visualization of Multiple Images by Nonlinear Projection Pursuit." Journal of the Institute of Image Information and Television Engineers 51, no. 10 (1997): 1777–80. http://dx.doi.org/10.3169/itej.51.1777.

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42

McClure, Kenneth S., R. Bhushan Gopaluni, Terrance Chmelyk, Devin Marshman, and Sirish L. Shah. "Nonlinear Process Monitoring Using Supervised Locally Linear Embedding Projection." Industrial & Engineering Chemistry Research 53, no. 13 (October 2, 2013): 5205–16. http://dx.doi.org/10.1021/ie401556r.

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43

Xia, Youshen, and Gang Feng. "A new neural network for solving nonlinear projection equations." Neural Networks 20, no. 5 (July 2007): 577–89. http://dx.doi.org/10.1016/j.neunet.2007.01.001.

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44

Voss, H. "Iterative Projection Methods for Large-Scale Nonlinear Eigenvalue Problems." Computational Technology Reviews 1 (September 14, 2010): 187–214. http://dx.doi.org/10.4203/ctr.1.7.

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45

Verma, Ram U. "General projection systems and relaxed cocoercive nonlinear variational inequalities." ANZIAM Journal 49, no. 2 (October 2007): 205–12. http://dx.doi.org/10.1017/s1446181100012785.

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AbstractWe explore the solvability of a general system of nonlinear relaxed cocoercive variational inequality (SNVI) problems based on a new projection system for the direct product of two nonempty closed and convex subsets of real Hilbert spaces.

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46

Martins, A. M., and J. T. Mendonça. "Projection-operator method for the nonlinear three-wave interaction." Physical Review A 31, no. 6 (June 1, 1985): 3898–906. http://dx.doi.org/10.1103/physreva.31.3898.

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47

Wu, Chenxia, Jianke Zhu, Deng Cai, Chun Chen, and Jiajun Bu. "Semi-Supervised Nonlinear Hashing Using Bootstrap Sequential Projection Learning." IEEE Transactions on Knowledge and Data Engineering 25, no. 6 (June 2013): 1380–93. http://dx.doi.org/10.1109/tkde.2012.76.

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48

Codecasa, Lorenzo. "Nonlinear dynamic compact thermal models by structure-preserving projection." Microelectronics Journal 45, no. 12 (December 2014): 1764–69. http://dx.doi.org/10.1016/j.mejo.2014.06.001.

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49

Kim, Kyoungok, and Jaewook Lee. "Nonlinear Dynamic Projection for Noise Reduction of Dispersed Manifolds." IEEE Transactions on Pattern Analysis and Machine Intelligence 36, no. 11 (November 1, 2014): 2303–9. http://dx.doi.org/10.1109/tpami.2014.2318727.

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50

Zhao, Shi Jian, Jie Zhang, Yong Mao Xu, and Zhi Hua Xiong. "Nonlinear Projection to Latent Structures Method and Its Applications." Industrial & Engineering Chemistry Research 45, no. 11 (May 2006): 3843–52. http://dx.doi.org/10.1021/ie0512340.

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Journal articles on the topic 'Nonlinear projection'

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