A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems

被引：8

作者：

Fischer, B

Hanke, M

Hochbruck, M

机构：

[1] UNIV KARLSRUHE, INST PRAKT MATH, D-76128 KARLSRUHE, GERMANY

[2] UNIV TUBINGEN, INST MATH, D-72076 TUBINGEN, GERMANY

[3] UNIV LUBECK, INST MATH, D-23560 LUBECK, GERMANY

来源：

NUMERICAL ALGORITHMS | 1996年 / 11卷 / 1-4期

关键词：

D O I：

10.1007/BF02142495

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

To design a conjugate-gradient type method for a given linear system one has to choose an inner product space and to compute residual polynomials which minimize the induced norm. Here we propose a unified treatment of this approach for symmetric linear systems. We mainly focus on indefinite and/or inconsistent systems.

引用

页码：181 / 187

页数：7

共 13 条

[1]

[Anonymous], USSR COMPUT MATH MAT

[2]

CALVETTI D, 1994, SIAM PROC S, P267

[3] ON THE SOLUTION OF SINGULAR LINEAR-SYSTEMS OF ALGEBRAIC EQUATIONS BY SEMIITERATIVE METHODS [J].

EIERMANN, M ;

MAREK, I ;

NIETHAMMER, W .

NUMERISCHE MATHEMATIK, 1988, 53 (03) :265-283

[4]

Fischer B, 1996, Tech. rep.

[5]

FREUND R. W., 1986, THESIS U WURZBURG

[6]

Golub GH., 1961, Numer Math, V3, P147, DOI [10.1007/BF01386013, DOI 10.1007/BF01386013]

[7]

HANKE M, IN PRESS PITMAN RES

[8]

Hanke M., 1993, ELECTRON T NUMER ANA, V1, P89

[9] METHODS OF CONJUGATE GRADIENTS FOR SOLVING LINEAR SYSTEMS [J].

HESTENES, MR ;

STIEFEL, E .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS, 1952, 49 (06) :409-436

[10] AN ITERATION METHOD FOR THE SOLUTION OF THE EIGENVALUE PROBLEM OF LINEAR DIFFERENTIAL AND INTEGRAL OPERATORS [J].

LANCZOS, C .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS, 1950, 45 (04) :255-282

← 1 2 →