Error analysis of Krylov methods in a nutshell

被引:17
作者
Hochbruck, M [1 ]
Lubich, C [1 ]
机构
[1] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany
关键词
Krylov subspace methods; conjugate-gradient-type methods; Arnoldi method; Lanczos method; error bounds;
D O I
10.1137/S1064827595290450
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Error and residual bounds for the matrix iteration methods BiCG, QMR, FOM, and GMRES are derived in a simple and unified way.
引用
收藏
页码:695 / 701
页数:7
相关论文
共 22 条
[2]   AN ANALYSIS OF THE COMPOSITE STEP BICONJUGATE GRADIENT-METHOD [J].
BANK, RE ;
CHAN, TF .
NUMERISCHE MATHEMATIK, 1993, 66 (03) :295-319
[3]  
BARTH T, 1994, P 10 INT S MATR AN P
[4]   A THEORETICAL COMPARISON OF THE ARNOLDI AND GMRES ALGORITHMS [J].
BROWN, PN .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1991, 12 (01) :58-78
[5]   ON SEMIITERATIVE METHODS GENERATED BY FABER POLYNOMIALS [J].
EIERMANN, M .
NUMERISCHE MATHEMATIK, 1989, 56 (2-3) :139-156
[6]   VARIATIONAL ITERATIVE METHODS FOR NONSYMMETRIC SYSTEMS OF LINEAR-EQUATIONS [J].
EISENSTAT, SC ;
ELMAN, HC ;
SCHULTZ, MH .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (02) :345-357
[7]   AN IMPLEMENTATION OF THE LOOK-AHEAD LANCZOS-ALGORITHM FOR NON-HERMITIAN MATRICES [J].
FREUND, RW ;
GUTKNECHT, MH ;
NACHTIGAL, NM .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1993, 14 (01) :137-158
[8]   QMR - A QUASI-MINIMAL RESIDUAL METHOD FOR NON-HERMITIAN LINEAR-SYSTEMS [J].
FREUND, RW ;
NACHTIGAL, NM .
NUMERISCHE MATHEMATIK, 1991, 60 (03) :315-339
[9]  
Freund RW., 1992, ACTA NUMER, V1, P57
[10]  
HOCHBRUCK M, 1997, IN PRESS SIAM J NUME