Augmented Block Householder Arnoldi method

被引：16

作者：

Baglama, James ^{[1
]}

机构：

[1] Univ Rhode Isl, Dept Math, Kingston, RI 02881 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2008年 / 429卷 / 10期

关键词：

Partial eigenvalue value decomposition; Restarted iterative method; Implicit shifts; Augmentation; Krylov; Householder;

D O I：

10.1016/j.laa.2007.12.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Computing the eigenvalues and eigenvectors of a large sparse nonsymmetric matrix arises in many applications and can be a very computationally challenging problem. In this paper we propose the Augmented Block Householder Arnoldi (ABHA) method that combines the advantages of a block routine with an augmented Krylov routine. A public domain MATLAB code ahbeigs has been developed and numerical experiments indicate that the code is competitive with other publicly available codes. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：2315 / 2334

页数：20

共 52 条

[1]

Anderson E, 1999, LAPACK USERS GUIDE

[2]

[Anonymous], 1997, ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, DOI 10.1137/1.9780898719628

[3] THE PRINCIPLE OF MINIMIZED ITERATIONS IN THE SOLUTION OF THE MATRIX EIGENVALUE PROBLEM [J].

ARNOLDI, WE .

QUARTERLY OF APPLIED MATHEMATICS, 1951, 9 (01) :17-29

[4] Augmented implicitly restarted Lanczos bidiagonalization methods [J].

Baglama, J ;

Reichel, L .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 27 (01) :19-42

[5] Algorithm 827: irbleigs: a MATLAB program for computing a few eigenpairs of a large sparse Hermitian matrix [J].

Baglama, J ;

Calvetti, D ;

Reichel, L .

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2003, 29 (03) :337-348

[6] IRBL: An implicitly restarted block-lanczos method for large-scale Hermitian eigenproblems [J].

Baglama, J ;

Calvetti, D ;

Reichel, L .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 24 (05) :1650-1677

[7] Dealing with linear dependence during the iterations of the restarted block Lanczos methods [J].

Baglama, J .

NUMERICAL ALGORITHMS, 2000, 25 (1-4) :23-36

[8] Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling [J].

Baglama, J ;

Calvetti, D ;

Reichel, L ;

Ruttan, A .

JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 146 (01) :203-226

[9]

BAGLAMA J., 1998, ELECTRON T NUMER ANA, V7, P124

[10] Restarted block Lanczos bidiagonalization methods [J].

Baglama, James ;

Reichel, Lothar .

NUMERICAL ALGORITHMS, 2006, 43 (03) :251-272

← 1 2 3 4 5 6 →