草图-选择-阿诺德工艺

IF 3 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Scientific Computing Pub Date : 2024-08-21 DOI:10.1137/23m1588007

Stefan Güttel, Igor Simunec

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引用次数: 0

摘要

SIAM 科学计算期刊》，第 46 卷第 4 期，第 A2774-A2797 页，2024 年 8 月。摘要。本文提出了一种 "草图-选择阿诺德过程"（sketch-and-select Arnoldi process），以低成本生成条件良好的克雷洛夫空间基。在每次迭代时，该过程利用随机草图选择有限数量的先前计算的基向量，以投影出当前的基向量。计算成本与克雷洛夫空间的维度呈线性增长。投影步骤的子集选择问题可以通过统计学习和压缩传感中使用的一些启发式算法和贪婪方法近似解决。计算结果的可重复性。本文被授予 "SIAM 可重现徽章"：代码和数据可用"，以表彰作者遵循了 SISC 和科学计算界重视的可重现性原则。读者可以通过 https://github.com/simunec/sketch-select-arnoldi 和补充材料（sketch-select-arnoldi-main.zip [2.21MB]）中的代码和数据重现本文的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Sketch-and-Select Arnoldi Process

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page A2774-A2797, August 2024.
Abstract. A sketch-and-select Arnoldi process to generate a well-conditioned basis of a Krylov space at low cost is proposed. At each iteration the procedure utilizes randomized sketching to select a limited number of previously computed basis vectors to project out of the current basis vector. The computational cost grows linearly with the dimension of the Krylov space. The subset selection problem for the projection step is approximately solved with a number of heuristic algorithms and greedy methods used in statistical learning and compressive sensing. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/simunec/sketch-select-arnoldi and in the supplementary materials (sketch-select-arnoldi-main.zip [2.21MB]).

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来源期刊

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.