RSMAR：范围对称线性系统的迭代方法

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-30 DOI:10.1016/j.laa.2025.09.024

Kui Du, Jia-Jun Fan, Fang Wang

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引用次数: 0

摘要

我们提出了一种新的迭代方法，命名为RSMAR（范围对称最小a -残差），用于求解范围对称线性系统（可能是奇异的）。RSMAR是Montoison， Orban和Saunders的MINARES方法的扩展[SIAM J. Matrix Anal]。达成。数学学报，46 (2025),pp. 509-529]。我们证明了在精确算法中，RSMAR和GMRES在应用于距离对称线性系统时具有相同的（最小二乘）解。在达到的最小二乘解不是伪逆解的情况下，我们证明了可以使用最小范数细化来获得伪逆解。我们提出了RSMAR的两种实现。我们的数值实验表明，RSMAR在奇异不一致距离对称线性系统上优于GMRES。

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RSMAR: An iterative method for range-symmetric linear systems

We propose a new iterative method, named RSMAR (Range-Symmetric Minimal A-Residual), for solving range-symmetric linear systems (possibly singular). RSMAR is an extension of the MINARES method of Montoison, Orban, and Saunders [SIAM J. Matrix Anal. Appl., 46 (2025), pp. 509–529] for solving symmetric linear systems. We prove that, in exact arithmetic, RSMAR and GMRES terminate with the same (least-squares) solution when applied to range-symmetric linear systems. In cases where the reached least-squares solution is not the pseudoinverse solution, we demonstrate that a minimum-norm refinement can be used to obtain the pseudoinverse solution. We present two implementations for RSMAR. Our numerical experiments show that RSMAR outperforms GMRES on singular inconsistent range-symmetric linear systems.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.