Relevant bibliographies by topics / Randomized iterative methods

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Randomized iterative methods'

Author: Grafiati
Published: 1 June 2024
Last updated: 31 July 2025

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Journal articles on the topic "Randomized iterative methods"

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Gower, Robert M., and Peter Richtárik. "Randomized Iterative Methods for Linear Systems." SIAM Journal on Matrix Analysis and Applications 36, no. 4 (2015): 1660–90. http://dx.doi.org/10.1137/15m1025487.

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Loizou, Nicolas, and Peter Richtárik. "Convergence Analysis of Inexact Randomized Iterative Methods." SIAM Journal on Scientific Computing 42, no. 6 (2020): A3979—A4016. http://dx.doi.org/10.1137/19m125248x.

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Xing, Lili, Wendi Bao, Ying Lv, Zhiwei Guo, and Weiguo Li. "Randomized Block Kaczmarz Methods for Inner Inverses of a Matrix." Mathematics 12, no. 3 (2024): 475. http://dx.doi.org/10.3390/math12030475.

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In this paper, two randomized block Kaczmarz methods to compute inner inverses of any rectangular matrix A are presented. These are iterative methods without matrix multiplications and their convergence is proved. The numerical results show that the proposed methods are more efficient than iterative methods involving matrix multiplications for the high-dimensional matrix.
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Zhao, Jing, Xiang Wang, and Jianhua Zhang. "Randomized average block iterative methods for solving factorised linear systems." Filomat 37, no. 14 (2023): 4603–20. http://dx.doi.org/10.2298/fil2314603z.

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Recently, some randomized iterative methods are proposed to solve large-scale factorised linear systems. In this paper, we present two randomized average block iterative methods which still take advantage of the factored form and need not perform the entire matrix. The new methods are pseudoinverse-free and can be implemented for parallel computation. Furthermore, we analyze their convergence behaviors and obtain the exponential convergence rate. Finally, some numerical examples are carried out to show the effectiveness of our new methods.
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Song, Hui, Wendi Bao, Lili Xing, and Weiguo Li. "On randomized multiple row-action methods for linear feasibility problems." Networks and Heterogeneous Media 19, no. 4 (2024): 1448–69. https://doi.org/10.3934/nhm.2024062.

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<p>In this paper, for solving linear feasibility problems we propose two randomized methods: a multiple row-action method (RMR) based on partial rows of residual vectors and its generalized method (GRMR) with history information in updating the current update. By introducing a linear combination of the information from the previous and subsequent iterative steps with the relaxation parameter $ \xi $, the GRMR method unifies various RMR-type algorithms. A thorough convergence analysis for the proposed methods is provided. The theoretical results show the theoretical convergence rate of th
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Zhang, Yanjun, and Hanyu Li. "Splitting-based randomized iterative methods for solving indefinite least squares problem." Applied Mathematics and Computation 446 (June 2023): 127892. http://dx.doi.org/10.1016/j.amc.2023.127892.

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Zheng, Wei, Lili Xing, Wendi Bao, and Weiguo Li. "Kaczmarz-Type Methods for Solving Matrix Equation AXB = C." Axioms 14, no. 5 (2025): 367. https://doi.org/10.3390/axioms14050367.

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This paper proposes a class of randomized Kaczmarz and Gauss–Seidel-type methods for solving the matrix equation AXB=C, where the matrices A and B may be either full-rank or rank deficient and the system may be consistent or inconsistent. These iterative methods offer high computational efficiency and low memory requirements, as they avoid costly matrix–matrix multiplications. We rigorously establish theoretical convergence guarantees, proving that the generated sequences converge to the minimal Frobenius-norm solution (for consistent systems) or the minimal Frobenius-norm least squares soluti
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Jensen, Erik, Evan C. Coleman, and Masha Sosonkina. "Implementing Asynchronous Linear Solvers Using Non-Uniform Distributions." Journal of Simulation Engineering 2 (July 31, 2020): 6:1–6:18. https://doi.org/10.5281/zenodo.11114215.

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Asynchronous iterative methods may improve the time-to-solution of their synchronous counterparts on highly parallel computational platforms. This paper considers asynchronous iterative linear system solvers that employ non-uniform randomization and develops a new implementation for such methods. Experiments with a two-dimensional finite-difference discrete Laplacian problem are presented. The new finer grain implementation is compared with an existing, block-based, one and shown to be superior in terms of the convergence speed and accuracy. In general, using non-uniform distributions in selec
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Yunak, O., M. Klymash, O. Shpur, and V. Mrak. "MATHEMATICAL MODEL OF FRACTAL STRUCTURES RECOGNITION USING NEURAL NETWORK TECHNOLOGY." Information and communication technologies, electronic engineering 3, no. 1 (2023): 1–9. http://dx.doi.org/10.23939/ictee2023.01.001.

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The article goes about the methods of training a neural network to recognize fractal structures with the rotation of iteration elements by means of an improved randomized system of iteration functions. Parameters of fractal structures are used to calculate complex parameters of physical phenomena. They are an effective tool in scientific works and used to calculate quantitative indicators in technical tasks. The calculation of these parameters is a very difficult mathematical problem. This is caused by the fact that it is very difficult to describe the mathematical model of the fractal image,
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Sabelfeld, Karl K. "Randomized Monte Carlo algorithms for matrix iterations and solving large systems of linear equations." Monte Carlo Methods and Applications 28, no. 2 (2022): 125–33. http://dx.doi.org/10.1515/mcma-2022-2114.

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Abstract Randomized scalable vector algorithms for calculation of matrix iterations and solving extremely large linear algebraic equations are developed. Among applications presented in this paper are randomized iterative methods for large linear systems of algebraic equations governed by M-matrices. The crucial idea of the randomized method is that the iterations are performed by sampling random columns only, thus avoiding not only matrix-matrix but also matrix-vector multiplications. The suggested vector randomized methods are highly efficient for solving linear equations of high dimension,
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Dissertations / Theses on the topic "Randomized iterative methods"

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Gower, Robert Mansel. "Sketch and project : randomized iterative methods for linear systems and inverting matrices." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20989.

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Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these ideas influence these fields is via the development and analysis of randomized algorithms for solving standard and new problems of these fields. Such methods are typically easier to analyze, and often lead to faster and/or more scalable and versatile methods in practice. This thesis explores the design and analysis of new randomized iterative methods for solv
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Bai, Xianglan. "Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919.

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UGWU, UGOCHUKWU OBINNA. "Iterative tensor factorization based on Krylov subspace-type methods with applications to image processing." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1633531487559183.

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Gazagnadou, Nidham. "Expected smoothness for stochastic variance-reduced methods and sketch-and-project methods for structured linear systems." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAT035.

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L'augmentation considérable du volume de données ainsi que de la taille des échantillons complexifie la phase d'optimisation des algorithmes d'apprentissage, nécessitant la minimisation d'une fonction de perte. La descente de gradient stochastique (SGD) et ses variantes à réduction de variance (SAGA, SVRG, MISO) sont largement utilisées pour résoudre ces problèmes. En pratique, ces méthodes sont accélérées en calculant des gradients stochastiques sur un "mini-batch" : un petit groupe d'échantillons tiré aléatoirement. En effet, les récentes améliorations technologiques permettant la parallélis
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Wu, Wei. "Paving the Randomized Gauss-Seidel." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/scripps_theses/1074.

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The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the
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Book chapters on the topic "Randomized iterative methods"

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Azzam, Joy, Benjamin W. Ong, and Allan A. Struthers. "Randomized Iterative Methods for Matrix Approximation." In Machine Learning, Optimization, and Data Science. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95470-3_17.

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Zhao, Xuefang. "A Randomized Iterative Approach for SV Discovery with SVelter." In Methods in Molecular Biology. Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4939-8666-8_13.

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Márquez, Airam Expósito, and Christopher Expósito-Izquierdo. "An Overview of the Last Advances and Applications of Greedy Randomized Adaptive Search Procedure." In Advances in Computational Intelligence and Robotics. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2857-9.ch013.

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One of the most studied methods to get approximate solutions in optimization problems are the heuristics methods. Heuristics are usually employed to find good, but not necessarily optima solutions. The primary purpose of the chapter at hand is to provide a survey of the Greedy Randomized Adaptive Search Procedures (GRASP). GRASP is an iterative multi-start metaheuristic for solving complex optimization problems. Each GRASP iteration consists of a construction phase followed by a local search procedure. In this paper, we first describe the basic components of GRASP and the various elements that
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Inchausti, Pablo. "The Generalized Linear Model." In Statistical Modeling With R. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192859013.003.0008.

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Abstract This chapter introduces the three components of a generalized linear model (GLM): the linear predictor, the link function, and the probability function. It discusses the exponential dispersion family as a generator model for GLMs in a large sense. It sketches the fitting of a GLM with the iteratively weighted least squares algorithm for maximum likelihood in the frequentist framework. It introduces the main methods for assessing the effects of explanatory variables in frequentist GLMs (the Wald and likelihood ratio tests), the use of deviance as a measure of lack of model fit in GLMs,
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Conference papers on the topic "Randomized iterative methods"

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Ding, Liyong, Enbin Song та Yunmin Zhu. "Accelerate randomized coordinate descent iterative hard thresholding methods for ℓ0 regularized convex problems". У 2016 35th Chinese Control Conference (CCC). IEEE, 2016. http://dx.doi.org/10.1109/chicc.2016.7553791.

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Carr, Steven, Nils Jansen, and Ufuk Topcu. "Verifiable RNN-Based Policies for POMDPs Under Temporal Logic Constraints." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/570.

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Recurrent neural networks (RNNs) have emerged as an effective representation of control policies in sequential decision-making problems. However, a major drawback in the application of RNN-based policies is the difficulty in providing formal guarantees on the satisfaction of behavioral specifications, e.g. safety and/or reachability. By integrating techniques from formal methods and machine learning, we propose an approach to automatically extract a finite-state controller (FSC) from an RNN, which, when composed with a finite-state system model, is amenable to existing formal verification tool
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Jahani, Nazanin, Joaquín Ambía, Kristian Fossum, Sergey Alyaev, Erich Suter, and Carlos Torres-Verdín. "REAL-TIME ENSEMBLE-BASED WELL-LOG INTERPRETATION FOR GEOSTEERING." In 2021 SPWLA 62nd Annual Logging Symposium Online. Society of Petrophysicists and Well Log Analysts, 2021. http://dx.doi.org/10.30632/spwla-2021-0105.

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The cost of drilling wells on the Norwegian Continen-tal Shelf are extremely high, and hydrocarbon reservoirs are often located in spatially complex rock formations. Optimized well placement with real-time geosteering is crucial to efficiently produce from such reservoirs and reduce exploration and development costs. Geosteering is commonly assisted by repeated formation evaluation based on the interpretation of well logs while drilling. Thus, reliable computationally efficient and robust work-flows that can interpret well logs and capture uncertain-ties in real time are necessary for successf
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Wei He, Hongyan Zhang, Liangpei Zhang, and Huanfeng Shen. "A noise-adjusted iterative randomized singular value decomposition method for hyperspectral image denoising." In IGARSS 2014 - 2014 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2014. http://dx.doi.org/10.1109/igarss.2014.6946731.

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Feng, Xu, and Wenjian Yu. "A Fast Adaptive Randomized PCA Algorithm." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/411.

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It is desirable to adaptively determine the number of dimensions (rank) for PCA according to a given tolerance of low-rank approximation error. In this work, we aim to develop a fast algorithm solving this adaptive PCA problem. We propose to replace the QR factorization in randQB_EI algorithm with matrix multiplication and inversion of small matrices, and propose a new error indicator to incrementally evaluate approximation error in Frobenius norm. Combining the shifted power iteration technique for better accuracy, we finally build up an algorithm named farPCA. Experimental results show that
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Kaushik, Harshal, and Farzad Yousefian. "A Randomized Block Coordinate Iterative Regularized Subgradient Method for High-dimensional Ill-posed Convex Optimization." In 2019 American Control Conference (ACC). IEEE, 2019. http://dx.doi.org/10.23919/acc.2019.8815256.

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Buermann, Jan, and Jie Zhang. "Multi-Robot Adversarial Patrolling Strategies via Lattice Paths." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/582.

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In full-knowledge multi-robot adversarial patrolling, a group of robots have to detect an adversary who knows the robots' strategy. The adversary can easily take advantage of any deterministic patrolling strategy, which necessitates the employment of a randomised strategy. While the Markov decision process has been the dominant methodology in computing the penetration detection probabilities, we apply enumerative combinatorics to characterise the penetration detection probabilities. It allows us to provide the closed formulae of these probabilities and facilitates characterising optimal random
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Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Mehrdad Karrabi, Petr Novotný, and Đorđe Žikelić. "Solving Long-run Average Reward Robust MDPs via Stochastic Games." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/741.

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Markov decision processes (MDPs) provide a standard framework for sequential decision making under uncertainty. However, MDPs do not take uncertainty in transition probabilities into account. Robust Markov decision processes (RMDPs) address this shortcoming of MDPs by assigning to each transition an uncertainty set rather than a single probability value. In this work, we consider polytopic RMDPs in which all uncertainty sets are polytopes and study the problem of solving long-run average reward polytopic RMDPs. We present a novel perspective on this problem and show that it can be reduced to s
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Xie, Jiarui, Chonghui Zhang, Lijun Sun, and Yaoyao Fiona Zhao. "Fairness- and Uncertainty-Aware Data Generation for Data-Driven Design." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-114687.

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Abstract The design dataset is the backbone of data-driven design. Ideally, the dataset should be fairly distributed in both shape and property spaces to efficiently explore the underlying relationship. However, the classical experimental design focuses on shape diversity and thus yields biased exploration in the property space. Recently developed methods either conduct subset selection from a large dataset or employ assumptions with severe limitations. In this paper, fairness- and uncertainty-aware data generation (FairGen) is proposed to actively detect and generate missing properties starti
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Gao, Guohua, Horacio Florez, Sean Jost, et al. "Implementation of Asynchronous Distributed Gauss-Newton Optimization Algorithms for Uncertainty Quantification by Conditioning to Production Data." In SPE Annual Technical Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/210118-ms.

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Abstract Previous implementation of distributed Gauss-Newton (DGN) optimization algorithm runs multiple optimization threads in parallel, employing a synchronous running mode (S-DGN). As a result, it waits for all simulations submitted in each iteration to complete, which may significantly degrade performance because a few simulations may run much longer than others, especially for time-consuming real-field cases. To overcome this limitation and thus improve the DGN optimizer's execution, we propose two asynchronous DGN (A-DGN) optimization algorithms in this paper. The A-DGN optimizer is a we
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