稀疏线性最小二乘问题

IF 11.3 1区数学 Q1 MATHEMATICS

Acta Numerica Pub Date : 2025-07-01 DOI:10.1017/s0962492924000059

Jennifer Scott, Miroslav Tůma

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引用次数: 0

摘要

最小二乘问题是计算科学和工程的基石。多年来，研究人员和实践者面临的问题规模不断增加，使得在解决方案过程中利用稀疏性变得至关重要。本文的目的是对解决大规模线性最小二乘问题的关键算法进行综述。这包括与迭代求解器结合使用的稀疏直接方法和代数预条件。在有软件可用的地方，这是突出显示的。

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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Sparse linear least-squares problems

Least-squares problems are a cornerstone of computational science and engineering. Over the years, the size of the problems that researchers and practitioners face has constantly increased, making it essential that sparsity is exploited in the solution process. The goal of this article is to present a broad review of key algorithms for solving large-scale linear least-squares problems. This includes sparse direct methods and algebraic preconditioners that are used in combination with iterative solvers. Where software is available, this is highlighted.

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来源期刊

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.