Journal articles: 'Iterators'

1

Baker, Henry G. "Iterators." ACM SIGPLAN OOPS Messenger 4, no. 3 (July 1993): 18–25. http://dx.doi.org/10.1145/165507.165514.

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Liu, Jed, Aaron Kimball, and Andrew C. Myers. "Interruptible iterators." ACM SIGPLAN Notices 41, no. 1 (January 12, 2006): 283–94. http://dx.doi.org/10.1145/1111320.1111063.

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3

Lamb, D. A. "Specification of iterators." IEEE Transactions on Software Engineering 16, no. 12 (1990): 1352–60. http://dx.doi.org/10.1109/32.62444.

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4

Castagna, Giuseppe, and Kim Nguyen. "Typed iterators for XML." ACM SIGPLAN Notices 43, no. 9 (September 27, 2008): 15–26. http://dx.doi.org/10.1145/1411203.1411210.

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MESSERSCHMIDT, H. J. "List Iterators in C++." Software: Practice and Experience 26, no. 11 (November 1996): 1197–203. http://dx.doi.org/10.1002/(sici)1097-024x(199611)26:11<1197::aid-spe55>3.0.co;2-l.

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Haack, Christian, and Clément Hurlin. "Resource Usage Protocols for Iterators." Journal of Object Technology 8, no. 4 (2009): 55. http://dx.doi.org/10.5381/jot.2009.8.4.a3.

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7

Coyle, Christopher, and Peter Crogono. "Building abstract iterators using continuations." ACM SIGPLAN Notices 26, no. 2 (January 2, 1991): 17–24. http://dx.doi.org/10.1145/122179.122181.

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Rayside, Derek, Vajihollah Montaghami, Francesca Leung, Albert Yuen, Kevin Xu, and Daniel Jackson. "Synthesizing iterators from abstraction functions." ACM SIGPLAN Notices 48, no. 3 (April 10, 2013): 31–40. http://dx.doi.org/10.1145/2480361.2371407.

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Zhang, Wei, Per Larsen, Stefan Brunthaler, and Michael Franz. "Accelerating iterators in optimizing AST interpreters." ACM SIGPLAN Notices 49, no. 10 (December 31, 2014): 727–43. http://dx.doi.org/10.1145/2714064.2660223.

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Bergstra, Jan A., and Alban Ponse. "Non-regular iterators in process algebra." Theoretical Computer Science 269, no. 1-2 (October 2001): 203–29. http://dx.doi.org/10.1016/s0304-3975(00)00413-8.

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Malykh, A. A., and A. V. Mantsivoda. "List Superstructures and Semantics of Iterators." Journal of Mathematical Sciences 203, no. 4 (October 31, 2014): 540–50. http://dx.doi.org/10.1007/s10958-014-2157-8.

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12

GRAEFE, GOETZ. "Iterators, Schedulers, and Distributed-memory Parallelism." Software: Practice and Experience 26, no. 4 (April 1996): 427–52. http://dx.doi.org/10.1002/(sici)1097-024x(199604)26:4<427::aid-spe20>3.0.co;2-h.

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13

Morel, Lionel. "Efficient compilation of array iterators for Lustre." Electronic Notes in Theoretical Computer Science 65, no. 5 (July 2002): 19–26. http://dx.doi.org/10.1016/s1571-0661(05)80437-2.

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14

Fatourou, Panagiota, Yiannis Nikolakopoulos, and Marina Papatriantafilou. "Linearizable Wait-Free Iteration Operations in Shared Double-Ended Queues." Parallel Processing Letters 27, no. 02 (June 2017): 1750001. http://dx.doi.org/10.1142/s0129626417500013.

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Shared data object implementations that allow non-blocking concurrent operations are useful for in-memory data-processing, especially when they support consistent bulk operations like iterations. We propose an algorithmic implementation for concurrent iterators on shared double-ended queues (deques), building on and complementing a known lock-free deque implementation by M. Michael. The proposed construction is linearizable and wait-free. Moreover, it is read-only, so it does not execute expensive synchronization primitives and it does not interfere with update operations.

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Heaney, Matthew. "Gem #9: Classwide operations, iterators, and generic algorithms." ACM SIGAda Ada Letters XXVIII, no. 1 (April 2008): 52–58. http://dx.doi.org/10.1145/1387830.1387846.

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Weide, B. W., S. H. Edwards, D. E. Harms, and D. A. Lamb. "Design and specification of iterators using the swapping paradigm." IEEE Transactions on Software Engineering 20, no. 8 (1994): 631–43. http://dx.doi.org/10.1109/32.310672.

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Müller, Mark Niklas, Marc Fischer, Robin Staab, and Martin Vechev. "Abstract Interpretation of Fixpoint Iterators with Applications to Neural Networks." Proceedings of the ACM on Programming Languages 7, PLDI (June 6, 2023): 786–810. http://dx.doi.org/10.1145/3591252.

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We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators. Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all reachable program states, in this setting, one only needs to abstract the concrete fixpoints, i.e., the final program states. Our framework targets numerical fixpoint iterators with convergence and uniqueness guarantees in the concrete and is based on two major technical contributions: (i) theoretical insights which allow us to compute sound and precise fixpoint abstractions without using joins, and (ii) a new abstract domain, CH-Zonotope, which admits efficient propagation and inclusion checks while retaining high precision. We implement our framework in a tool called CRAFT and evaluate it on a novel fixpoint-based neural network architecture (monDEQ) that is particularly challenging to verify. Our extensive evaluation demonstrates that CRAFT exceeds the state-of-the-art performance in terms of speed (two orders of magnitude), scalability (one order of magnitude), and precision (25% higher certified accuracies).

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Mosteo, Alejandro R., and María-Teresa Lorente. "Exploring the boundaries of Ada syntax with functional-style iterators." Journal of Systems Architecture 116 (June 2021): 102039. http://dx.doi.org/10.1016/j.sysarc.2021.102039.

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Peschanski, Frédéric, Hanna Klaudel, and Raymond Devillers. "A Decidable Characterization of a Graphical Pi-calculus with Iterators." Electronic Proceedings in Theoretical Computer Science 39 (October 28, 2010): 47–61. http://dx.doi.org/10.4204/eptcs.39.4.

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20

Iannello, Giulio. "Programming abstract data types, iterators and generic modules in C." Software: Practice and Experience 20, no. 3 (March 1990): 243–60. http://dx.doi.org/10.1002/spe.4380200303.

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21

Tang, Xiaolong, and Jaakko Järvi. "Summary-based data-flow analysis that understands regular composite objects and iterators." ACM SIGAPP Applied Computing Review 12, no. 4 (December 2012): 36–47. http://dx.doi.org/10.1145/2432546.2432549.

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Morel, Lionel. "Array Iterators in Lustre: From a Language Extension to Its Exploitation in Validation." EURASIP Journal on Embedded Systems 2007 (2007): 1–16. http://dx.doi.org/10.1155/2007/59130.

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Morel, Lionel. "Array Iterators in Lustre: From a Language Extension to Its Exploitation in Validation." EURASIP Journal on Embedded Systems 2007, no. 1 (2007): 059130. http://dx.doi.org/10.1186/1687-3963-2007-059130.

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24

Baglio, S., L. Fortuna, and G. Manganaro. "Design of fuzzy iterators to generate chaotic time series with assigned Lyapunov exponent." Electronics Letters 32, no. 4 (1996): 292. http://dx.doi.org/10.1049/el:19960270.

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25

Al-Sibahi, Ahmad Salim, Thomas P. Jensen, Aleksandar S. Dimovski, and Andrzej Wąsowski. "Verification of Program Transformations with Inductive Refinement Types." ACM Transactions on Software Engineering and Methodology 30, no. 1 (January 21, 2021): 1–33. http://dx.doi.org/10.1145/3409805.

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High-level transformation languages like Rascal include expressive features for manipulating large abstract syntax trees: first-class traversals, expressive pattern matching, backtracking, and generalized iterators. We present the design and implementation of an abstract interpretation tool, Rabit, for verifying inductive type and shape properties for transformations written in such languages. We describe how to perform abstract interpretation based on operational semantics, specifically focusing on the challenges arising when analyzing the expressive traversals and pattern matching. Finally, we evaluate Rabit on a series of transformations (normalization, desugaring, refactoring, code generators, type inference, etc.) showing that we can effectively verify stated properties.

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26

Steere, David C. "Exploiting the non-determinism and asynchrony of set iterators to reduce aggregate file I/O latency." ACM SIGOPS Operating Systems Review 31, no. 5 (December 1997): 252–63. http://dx.doi.org/10.1145/269005.266705.

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27

Rodríguez, Abdel, Peter Vrancx, Ricardo Grau, and Ann Nowé. "A reinforcement learning approach to coordinate exploration with limited communication in continuous action games." Knowledge Engineering Review 31, no. 1 (January 2016): 77–95. http://dx.doi.org/10.1017/s026988891500020x.

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AbstractLearning automata are reinforcement learners belonging to the class of policy iterators. They have already been shown to exhibit nice convergence properties in a wide range of discrete action game settings. Recently, a new formulation for a continuous action reinforcement learning automata (CARLA) was proposed. In this paper, we study the behavior of these CARLA in continuous action games and propose a novel method for coordinated exploration of the joint-action space. Our method allows a team of independent learners, using CARLA, to find the optimal joint action in common interest settings. We first show that independent agents using CARLA will converge to a local optimum of the continuous action game. We then introduce a method for coordinated exploration which allows the team of agents to find the global optimum of the game. We validate our approach in a number of experiments.

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Alves, A. Augusto, Anton Poctarev, and Ralf Ulrich. "Counter-based pseudorandom number generators for CORSIKA 8." EPJ Web of Conferences 251 (2021): 03039. http://dx.doi.org/10.1051/epjconf/202125103039.

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This document is devoted to the description of advances in the generation of high-quality random numbers for CORSIKA 8, which is being developed in modern C++17 and is designed to run on modern multi-thread processors and accelerators. CORSIKA 8 is a Monte Carlo simulation framework to model ultra-high energy secondary particle cascades in astroparticle physics. The aspects associated with the generation of high-quality random numbers on massively parallel platforms, like multi-core CPUs and GPUs, are reviewed and the deployment of counter-based engines using an innovative and multi-thread friendly API are described. The API is based on iterators providing a very well known access mechanism in C++, and also supports lazy evaluation. Moreover, an upgraded version of the Squares algorithm with highly efficient internal 128 as well as 256 bit counters is presented in this context. Performance measurements are provided, as well as comparisons with conventional designs are given. Finally, the integration into CORSIKA 8 is commented.

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Moreno, J. "An infinite family of one-step iterators for solving nonlinear equations to increase the order of convergence and a new algorithm of global convergence." Computers & Mathematics with Applications 66, no. 8 (November 2013): 1418–36. http://dx.doi.org/10.1016/j.camwa.2013.08.003.

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30

Müller, Ingo, Ghislain Fourny, Stefan Irimescu, Can Berker Cikis, and Gustavo Alonso. "Rumble." Proceedings of the VLDB Endowment 14, no. 4 (December 2020): 498–506. http://dx.doi.org/10.14778/3436905.3436910.

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This paper introduces Rumble, a query execution engine for large, heterogeneous, and nested collections of JSON objects built on top of Apache Spark. While data sets of this type are more and more wide-spread, most existing tools are built around a tabular data model, creating an impedance mismatch for both the engine and the query interface. In contrast, Rumble uses JSONiq, a standardized language specifically designed for querying JSON documents. The key challenge in the design and implementation of Rumble is mapping the recursive structure of JSON documents and JSONiq queries onto Spark's execution primitives based on tabular data frames. Our solution is to translate a JSONiq expression into a tree of iterators that dynamically switch between local and distributed execution modes depending on the nesting level. By overcoming the impedance mismatch in the engine , Rumble frees the user from solving the same problem for every single query, thus increasing their productivity considerably. As we show in extensive experiments, Rumble is able to scale to large and complex data sets in the terabyte range with a similar or better performance than other engines. The results also illustrate that Codd's concept of data independence makes as much sense for heterogeneous, nested data sets as it does on highly structured tables.

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Phipps-Costin, Luna, Andreas Rossberg, Arjun Guha, Daan Leijen, Daniel Hillerström, KC Sivaramakrishnan, Matija Pretnar, and Sam Lindley. "Continuing WebAssembly with Effect Handlers." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (October 16, 2023): 460–85. http://dx.doi.org/10.1145/3622814.

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WebAssembly (Wasm) is a low-level portable code format offering near native performance. It is intended as a compilation target for a wide variety of source languages. However, Wasm provides no direct support for non-local control flow features such as async/await, generators/iterators, lightweight threads, first-class continuations, etc. This means that compilers for source languages with such features must ceremoniously transform whole source programs in order to target Wasm. We present WasmFX an extension to Wasm which provides a universal target for non-local control features via effect handlers, enabling compilers to translate such features directly into Wasm. Our extension is minimal and only adds three main instructions for creating, suspending, and resuming continuations. Moreover, our primitive instructions are type-safe providing typed continuations which are well-aligned with the design principles of Wasm whose stacks are typed. We present a formal specification of WasmFX and show that the extension is sound. We have implemented WasmFX as an extension to the Wasm reference interpreter and also built a prototype WasmFX extension for Wasmtime, a production-grade Wasm engine, piggybacking on Wasmtime's existing fibers API. The preliminary performance results for our prototype are encouraging, and we outline future plans to realise a native implementation.

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Hnatkowska, Bogumiła, and Bartosz Krych. "Comparing the understandability of iteration mechanisms over Collections in Java." Foundations of Computing and Decision Sciences 48, no. 1 (March 1, 2023): 19–37. http://dx.doi.org/10.2478/fcds-2023-0002.

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Abstract Source code understandability is a desirable quality factor affecting long-term code maintenance. Understandability of source code can be assessed in a variety of ways, including subjective evaluation of code fragments (perceived understandability), correctness, and response time to tasks performed. It can also be assessed using various source code metrics, such as cyclomatic complexity or cognitive complexity. Programming languages are evolving, giving programmers new ways to do the same things, e.g., iterating over collections. Functional solutions (lambda expressions and streams) are added to typical imperative constructs like iterators or for-each statements. This research aims to check if there is a correlation between perceived understandability, understandability measured by task correctness, and predicted by source code metrics for typical tasks that require iteration over collections implemented in Java. The answer is based on the results of an experiment. The experiment involved 99 participants of varying ages, declared Java knowledge and seniority measured in years. Functional code was perceived as the most understandable, but only in one case, the subjective assessment was confirmed by the correctness of answers. In two examples with the highest perceived understandability, streams received the worst correctness scores. Cognitive complexity and McCabe’s complexity had the lowest values in all tasks for the functional approach, but – unfortunately – they did not correlate with answer correctness. The main finding is that the functional approach to collection manipulation is the best choice for the filter-map-reduce idiom and its alternatives (e.g., filter-only). It should not be used in more complex tasks, especially those with higher complexity metrics.

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Sun, Ao, Qiuzhao Zhang, Zhangjun Yu, Xiaolin Meng, Xin Liu, Yunlong Zhang, and Yilin Xie. "A Novel Slow-Growing Gross Error Detection Method for GNSS/Accelerometer Integrated Deformation Monitoring Based on State Domain Consistency Theory." Remote Sensing 14, no. 19 (September 23, 2022): 4758. http://dx.doi.org/10.3390/rs14194758.

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The accuracy and integrity of structural deformation monitoring can be improved by the GNSS/accelerometer integrated system, and gross error detection is the key to further improving the reliability of GNSS/accelerometer monitoring. Traditional gross error detection methods assume that real-state information is known, and they need to establish state iterators, which leads to low computational efficiency. Meanwhile, in multi-sensor fusion, if the sampling rates are different, the change in the dimension of the observation matrix must be considered, and the calculation is complex. Based on state-domain consistency theory, this paper proposes the State-domain Robust Autonomous Integrity Monitoring by Extrapolation (SRAIME) method for identifying slow-growing gross errors for GNSS/accelerometer integrated deformation monitoring. Compared with the traditional gross error detection method, the proposed method constructs state test statistics based on the state estimated value and the state predicted value, and it directly performs gross error identification in the state domain. This paper deduces the feasibility of the proposed method theoretically and verifies that the proposed method does not need to consider the dimension change of the observation matrix in gross error detection. Meanwhile, in the excitation deformation experiments of the Suntuan River Bridge in Anhui and the Wilford Bridge in the United Kingdom, the slow gradient of the slope was added to the measurement domain, and the traditional AIME method and the method proposed in this paper were adopted for the gross error identification of the GNSS/accelerometer fusion process. The results demonstrate that both methods can effectively detect gross errors, but the proposed method does not need to consider the dimensional change in the observation matrix during the fusion process, which has better applicability to GNSS/accelerometer integrated deformation monitoring.

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GIBBONS, JEREMY, and BRUNO C. d. S. OLIVEIRA. "The essence of the Iterator pattern." Journal of Functional Programming 19, no. 3-4 (July 2009): 377–402. http://dx.doi.org/10.1017/s0956796809007291.

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AbstractThe Iterator pattern gives a clean interface for element-by-element access to a collection, independent of the collection's shape. Imperative iterations using the pattern have two simultaneous aspects: mapping and accumulating. Various existing functional models of iteration capture one or other of these aspects, but not both simultaneously. We argue that C. McBride and R. Paterson's applicative functors (Applicative programming with effects, J. Funct. Program., 18 (1): 1–13, 2008), and in particular the corresponding traverse operator, do exactly this, and therefore capture the essence of the Iterator pattern. Moreover, they do so in a way that nicely supports modular programming. We present some axioms for traversal, discuss modularity concerns and illustrate with a simple example, the wordcount problem.

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35

Revol, Nathalie. "Affine Iterations and Wrapping Effect." Acta Cybernetica 26, no. 1 (June 2, 2023): 129–47. http://dx.doi.org/10.14232/actacyb.295251.

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Affine iterations of the form xn+1=Axn+b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these iterations, in particular if the spectral radius of the absolute value of A is greater than 1. We will review different approaches to limit the overestimation of the iterates, when the components of the initial vector x(0) and b are intervals. We will compare, both theoretically and experimentally, the widths of the iterates computed by these different methods: the naive iteration, methods based on the QR- and SVD-factorization of A, and Lohner's QR-factorization method. The method based on the SVD-factorization is computationally less demanding and gives good results when the matrix is poorly scaled, it is superseded either by the naive iteration or by Lohner's method otherwise.

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Nasikun, Ahmad, and Klaus Hildebrandt. "The Hierarchical Subspace Iteration Method for Laplace–Beltrami Eigenproblems." ACM Transactions on Graphics 41, no. 2 (April 30, 2022): 1–14. http://dx.doi.org/10.1145/3495208.

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Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace–Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The Subspace Iteration Method is a robust solver for these problems. In practice, however, Lanczos schemes are often faster. In this article, we introduce the Hierarchical Subspace Iteration Method (HSIM) , a novel solver for sparse eigenproblems that operates on a hierarchy of nested vector spaces. The hierarchy is constructed such that on the coarsest space all eigenpairs can be computed with a dense eigensolver. HSIM uses these eigenpairs as initialization and iterates from coarse to fine over the hierarchy. On each level, subspace iterations, initialized with the solution from the previous level, are used to approximate the eigenpairs. This approach substantially reduces the number of iterations needed on the finest grid compared to the non-hierarchical Subspace Iteration Method. Our experiments show that HSIM can solve Laplace–Beltrami eigenproblems on meshes faster than state-of-the-art methods based on Lanczos iterations, preconditioned conjugate gradients, and subspace iterations.

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37

Fathi Al-Rubaie, Omar Ahmed, and Esam Mohammed Sheet Hamid. "Use a Mixture of Wood Lignin and Some Fertilizer to Improve the Chemical Content of Olive Seedlings." IOP Conference Series: Earth and Environmental Science 1060, no. 1 (July 1, 2022): 012055. http://dx.doi.org/10.1088/1755-1315/1060/1/012055.

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Abstract The study was conducted during the season 2021-2020 and was distributed on two main axes: the first is to extract the lignin from the trees of Milea azedarach L. The extraction process was carried out in the chemistry laboratory belonging to the College of agricultural technology/Mosul according to the basic method used in the manufacture of paper and paper paste. the second is the selection of one of the olive fields in the Nineveh forest nursery belonging to the Department of Agriculture of Nineveh and combating desertification, to find out the effect of the extract of lignin added to types of fertilizers and the overlap between them in the chemical content of the leaves. The three-factor experiment with three iterators was designed according to the design of complete random sectors (RCBD), This experiment was carried out on her from the cuttings of olive cultivar Arbequina if the factor on the concentrations of the extract accent (0,60%), while the second three types of fertilizer(compound fertilizer NPK, fertilizer nitrogen of Urea, compost mixture (Urea50%+NPK50%), the second factor was four levels of the proportion of mixing shellac with the quality( 0,10%,15%,25%), Proceedings of the spraying process early in the morning until the pallet is full, using the spray device sales capacity 2 liters. The results of the study showed that the treatment of seedlings with lignin extract concentration (60%) has a significant effect on both the content of the leaves (percentage of nitrogen, percentage of phosphorus, percentage of potassium), while the treatment with compound fertilizer was superior and at a concentration of 129 g.l-1significant in the percentage of carbohydrates, and to spray the olive seedlings with nitrogen fertilizer (Urea) especially the concentration of 10 g.l-1 While the treatment with mixed fertilizer (NPK 50%+ Urea 50%) showed significant effects in most of the studied chemical qualities, as for the two-and three-way interactions of the study transactions gave a significant effect in improving all the chemical qualities of the leaves and various concentrations, which led to the emergence of positive effects on the seedlings of olive trees for the transactions understudy, which led to increased activity and growth of seedlings throughout the research period.

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Xu, Helen, Amanda Li, Brian Wheatman, Manoj Marneni, and Prashant Pandey. "BP-Tree: Overcoming the Point-Range Operation Tradeoff for In-Memory B-Trees." Proceedings of the VLDB Endowment 16, no. 11 (July 2023): 2976–89. http://dx.doi.org/10.14778/3611479.3611502.

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B-trees are the go-to data structure for in-memory indexes in databases and storage systems. B-trees support both point operations (i.e., inserts and finds) and range operations (i.e., iterators and maps). However, there is an inherent tradeoff between point and range operations since the optimal node size for point operations is much smaller than the optimal node size for range operations. Existing implementations use a relatively small node size to achieve fast point operations at the cost of range operation throughput. We present the BP-tree , a variant of the B-tree, that overcomes the decades-old point-range operation tradeoff in traditional B-trees. In the BP-tree, the leaf nodes are much larger in size than the internal nodes to support faster range scans. To avoid any slowdown in point operations due to large leaf nodes, we introduce a new insert-optimized array called the buffered partitioned array (BPA) to efficiently organize data in leaf nodes. The BPA supports fast insertions by delaying ordering the keys in the array. This results in much faster range operations and faster point operations at the same time in the BP-tree. Our experiments show that on 48 hyperthreads, on workloads generated from the Yahoo! Cloud Serving Benchmark (YCSB), the BP-tree supports similar or faster point operation throughput (between .94×-1.2× faster) compared to Masstree and OpenBw-tree, two state-of-the-art in-memory key-value (KV) stores. On a YCSB workload with short scans, the BP-tree is about 7.4× faster than Masstree and 1.6× faster than OpenBw-tree. Furthermore, we extend the YCSB to add large range workloads, commonly found in database applications, and show that the BP-tree is 30× faster than Masstree and 2.5× faster than OpenBw-tree. We also provide a reference implementation for a concurrent B + -tree and find that the BP-tree supports faster (between 1.03×-1.2× faster) point operations when compared to the best-case configuration for B + -trees for point operations while supporting similar performance (about .95× as fast) on short range operations and faster (about 1.3× faster) long range operations.

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39

Weigert, F. J. "A gear iterator." Computers & Chemistry 11, no. 4 (January 1987): 273–80. http://dx.doi.org/10.1016/0097-8485(87)85005-2.

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40

KAUFMANN, LUCAS. "Commuting pairs of endomorphisms of." Ergodic Theory and Dynamical Systems 38, no. 3 (September 19, 2016): 1025–47. http://dx.doi.org/10.1017/etds.2016.54.

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We consider commuting pairs of holomorphic endomorphisms of $\mathbb{P}^{2}$ with disjoint sequence of iterates. The case that has not been completely studied is when their degrees coincide after some number of iterations. We show in this case that they are either commuting Lattès maps or commuting homogeneous polynomial maps of $\mathbb{C}^{2}$ inducing a Lattès map on the line at infinity.

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41

Hartfiel, D. J. "Boxed iterations." Applied Mathematics and Computation 143, no. 1 (October 2003): 61–71. http://dx.doi.org/10.1016/s0096-3003(02)00344-2.

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42

O'Connell, Megan. "Multifold Iterations." International Journal of the Book 4, no. 4 (2007): 177–84. http://dx.doi.org/10.18848/1447-9516/cgp/v04i04/36652.

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43

Heffernan, Tara. "Current Iterations." Journal of Australian Studies 43, no. 3 (July 3, 2019): 398–99. http://dx.doi.org/10.1080/14443058.2019.1649799.

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44

Moraru, Christian. "Critical Iterations." American Book Review 28, no. 3 (2007): 8–9. http://dx.doi.org/10.1353/abr.2007.0080.

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Wittum, G. "Shifted iterations." Numerische Mathematik 76, no. 2 (April 1, 1997): 265–78. http://dx.doi.org/10.1007/s002110050263.

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46

Briggs, Keith. "Hypercomplex iterations." Mathematical Intelligencer 26, no. 2 (March 2004): 74–75. http://dx.doi.org/10.1007/bf02985661.

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47

Scholz, H. J. "Phyllotactic Iterations." Berichte der Bunsengesellschaft für physikalische Chemie 89, no. 6 (June 1985): 699–703. http://dx.doi.org/10.1002/bbpc.19850890624.

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Ceng, Lu-Chuan, Jen-Chih Yao, and Yekini Shehu. "On Mann-Type Subgradient-like Extragradient Method with Linear-Search Process for Hierarchical Variational Inequalities for Asymptotically Nonexpansive Mappings." Mathematics 9, no. 24 (December 20, 2021): 3322. http://dx.doi.org/10.3390/math9243322.

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We propose two Mann-type subgradient-like extra gradient iterations with the line-search procedure for hierarchical variational inequality (HVI) with the common fixed-point problem (CFPP) constraint of finite family of nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. Our methods include combinations of the Mann iteration method, subgradient extra gradient method with the line-search process, and viscosity approximation method. Under suitable assumptions, we obtain the strong convergence results of sequence of iterates generated by our methods for a solution to HVI with the CFPP constraint.

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De la Sen, M. "On Best Proximity Point Theorems and Fixed Point Theorems for -Cyclic Hybrid Self-Mappings in Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/183174.

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This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent -hybrid -cyclic self-mappings relative to a Bregman distance , associated with a Gâteaux differentiable proper strictly convex function in a smooth Banach space, where the real functions and quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping. Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

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50

Yadav, Hema, Shoyeb Ali Sayyed, and V. H. Badshah. "A note on common fixed point theorem in Hilbert Space." Material Science Research India 7, no. 2 (February 8, 2010): 515–18. http://dx.doi.org/10.13005/msri/070226.

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In this paper the authors studied the problem of Sayyed and Badshah8 and prove common fixed point theorem in Hilbert Space. In recent years Rashwan and Sadik5, Malnge3, Berinde1, Rashwan4, Song and Chen11, Cric, Ume and Khan2 have studied the convergence of iterations to common fixed point for a pair of mappings. Rhoades6-7, proved the mappings T satisfying certain contractive condition, if the sequences of Mann iterates converged it converges to a fixed point of T. Sayyed and Badshah9-10 proved generalized contractive type mapping in Hilbert Space. AMS (2000) Subject Classifications: Primary 47H10, Secondary 54H25

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Journal articles on the topic 'Iterators'

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