线性系统和特征值问题的快速准确随机算法

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-06-20 DOI:10.1137/23m1565413

Yuji Nakatsukasa, Joel A. Tropp

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引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷，第 2 期，第 1183-1214 页，2024 年 6 月。摘要本文针对一般线性系统和特征值问题开发了一类算法。这些算法采用快速随机降维（"勾勒"）来加速标准子空间投影方法，如 GMRES 和 Rayleigh-Ritz。通过这种修改，可以为近似子空间加入更容易构建的非传统基。当基在数值上是满级时，新算法的精度与经典方法相似，但运行速度更快，使用的存储空间也更少。对于模型问题，数值实验表明，优化后的 MATLAB 例程具有很大优势，包括比[math]快[math]，比[math]快[math]。

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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Fast and Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 2, Page 1183-1214, June 2024.
Abstract. This paper develops a class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized dimension reduction (“sketching”) to accelerate standard subspace projection methods, such as GMRES and Rayleigh–Ritz. This modification makes it possible to incorporate nontraditional bases for the approximation subspace that are easier to construct. When the basis is numerically full rank, the new algorithms have accuracy similar to classic methods but run faster and may use less storage. For model problems, numerical experiments show large advantages over the optimized MATLAB routines, including a [math] speedup over [math] and a [math] speedup over [math].

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.