ANALYSIS OF THE TRUNCATED CONJUGATE GRADIENT METHOD FOR LINEAR MATRIX EQUATIONS

被引：8

作者：

Simoncini, Valeria ^{[1
,2
,3
]}

Hao, Yue ^{[4
]}

机构：

[1] Alma Mater Studiorum Univ Bologna, Dipartimento Matemat & AM2, Piazza Porta S Donato 5, I-40127 Bologna, Italy

[2] IMATI CNR, Pavia, Italy

[3] IAC CNR, Bari, Italy

[4] Inst Appl Phys & Computat Math, High Performance Comp Ctr, Beijing 100088, Peoples R China

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2023年 / 44卷 / 01期

基金：

海南省自然科学基金; 中国国家自然科学基金;

关键词：

conjugate gradients; linear matrix equations; truncation strategies; low-rank methods; KRYLOV SUBSPACE METHODS; LOW-RANK METHODS; LYAPUNOV EQUATIONS; SYSTEMS; LANCZOS;

D O I：

10.1137/22M147880X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The matrix-oriented version of the conjugate gradient (CG) method can be used to approximate the solution to certain linear matrix equations. To limit memory consumption, low -rank reduction of the factored iterates is often employed, possibly leading to disruption of the regular convergence behavior. We analyze the properties of the method in the matrix regime and identify the quantities that are responsible for early termination, usually stagnation, when truncation is in effect. Moreover, we illustrate relations between CG and a projection technique directly applied to the same matrix equation.

引用

收藏

页码：359 / 381

页数：23

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