Some preconditioning techniques for a class of double saddle point problems

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-02-22 DOI:10.1002/nla.2551

Fariba Balani Bakrani, Luca Bergamaschi, Ángeles Martínez, Masoud Hajarian

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引用次数: 0

Abstract

In this paper, we describe and analyze the spectral properties of several exact block preconditioners for a class of double saddle point problems. Among all these, we consider an inexact version of a block triangular preconditioner providing extremely fast convergence of the (F)GMRES method. We develop a spectral analysis of the preconditioned matrix showing that the complex eigenvalues lie in a circle of center

(1, 0) $$ \left(1,0\right) $$

and radius 1, while the real eigenvalues are described in terms of the roots of a third order polynomial with real coefficients. Numerical examples are reported to illustrate the efficiency of inexact versions of the proposed preconditioners, and to verify the theoretical bounds.

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一类双鞍点问题的一些预处理技术

在本文中，我们描述并分析了针对一类双鞍点问题的几种精确块预处理的光谱特性。其中，我们考虑了一种非精确版的块三角形预调器，它能使 (F)GMRES 方法极速收敛。我们对预处理矩阵进行了频谱分析，结果表明复特征值位于以 (1,0)$$ \left(1,0\right) $$ 为圆心、以 1 为半径的圆内，而实特征值则用具有实系数的三阶多项式的根来描述。报告中的数值示例说明了所提出的非精确版本预处理器的效率，并验证了理论边界。

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

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.