PRECONDITIONERS FOR SYMMETRIZED TOEPLITZ AND MULTILEVEL TOEPLITZ MATRICES

被引：16

作者：

Pestana, J. ^{[1
]}

机构：

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2019年 / 40卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Toeplitz matrix; multilevel Toeplitz matrix; symmetrization; preconditioning; Krylov subspace method; FINITE-DIFFERENCE APPROXIMATIONS; CIRCULANT PRECONDITIONERS; SPECTRAL-ANALYSIS; CONVERGENCE; STRATEGIES; ALGORITHM; SYSTEMS;

D O I：

10.1137/18M1205406

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized system, which allows rigorous upper bounds on the number of MINRES iterations to be obtained. However, effective preconditioners for symmetrized (multilevel) Toeplitz matrices are lacking. Here, we propose novel ideal preconditioners and investigate the spectra of the preconditioned matrices. We show how these preconditioners can be approximated and demonstrate their effectiveness via numerical experiments.

引用

页码：870 / 887

页数：18

共 48 条

[1]

[Anonymous], 1985, Matrix Analysis

[2] Krylov sequences of maximal length and convergence of GMRES [J].

Arioli, M ;

Pták, V ;

Strakos, Z .

BIT, 1998, 38 (04) :636-643

[3] ON BILINEAR-FORMS IN GAUSSIAN RANDOM-VARIABLES AND TOEPLITZ MATRICES [J].

AVRAM, F .

PROBABILITY THEORY AND RELATED FIELDS, 1988, 79 (01) :37-45

[4]

Breiten T, 2016, ELECTRON T NUMER ANA, V45, P107

[5]

Capizzano SS, 2002, LINEAR ALGEBRA APPL, V343, P303

[6] How to prove that a preconditioner cannot be superlinear [J].

Capizzano, SS ;

Tyrtyshnikov, E .

MATHEMATICS OF COMPUTATION, 2003, 72 (243) :1305-1316

[7]

Chan Raymond Hon-Fu., 2007, Society for Industrial and Applied Mathematics, DOI [DOI 10.1137/1.9780898718850, 10.1137/1.9780898718850]

[8] CIRCULANT PRECONDITIONERS CONSTRUCTED FROM KERNELS [J].

CHAN, RH ;

YEUNG, MC .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (04) :1093-1103

[9] TOEPLITZ PRECONDITIONERS FOR HERMITIAN TOEPLITZ-SYSTEMS [J].

CHAN, RH ;

NG, KP .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1993, 190 :181-208

[10]

Chan RH, 1996, NUMER LINEAR ALGEBR, V3, P45, DOI 10.1002/(SICI)1099-1506(199601/02)3:1<45::AID-NLA70>3.0.CO

← 1 2 3 4 5 →