Improved error bounds for the deflated multi-preconditioned CG method

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-02-25 DOI:10.1016/j.laa.2025.02.022

Reinhard Nabben, Julian Schramm

引用次数: 0

Abstract

Preconditioning and deflation are well-known techniques to speed up the convergence of the CG method. The concept of multiple-preconditioning however is introduced in the last decade. Recently, in [21], a new adaptive preconditioned CG method is established that combines all these techniques. The main tool of the adaptive method is a new error bound for the deflated preconditioned CG method. Using this bound it is decided in each iteration if the deflated preconditioned CG method is sufficient in reducing the error or whether an acceleration by performing iterations of the multi-preconditioned CG method is needed. Here we improve this error bound. This new bound contributes to the theory of deflation methods but can also lead to new decision rules for the adaptive multi-preconditioned CG method.

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改进了放气多预条件CG方法的误差界

预处理和通货紧缩是众所周知的加速CG方法收敛的技术。然而，多重预处理的概念是近十年来引入的。最近，在[21]中，建立了一种新的自适应预置CG方法，将这些技术结合在一起。自适应方法的主要工具是对放气预处理CG方法提出新的误差界。使用这个边界，在每次迭代中决定是否压缩预条件CG方法足以减小误差，或者是否需要通过执行多预条件CG方法的迭代来加速。这里我们改进了误差界。这一新的边界不仅有助于通货紧缩方法理论的发展，而且还可以为自适应多前提CG方法提供新的决策规则。

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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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.