On twisted factorizations of block tridiagonal matrices

被引：2
作者：
Gansterer, Wilfried N. [1 ]
Koenig, Gerhard [2 ]
机构：
[1] Univ Vienna, Res Lab Computat Technol & Applicat, A-1010 Vienna, Austria
[2] Univ Vienna, Dept Computat Biolog Chem, A-1010 Vienna, Austria
来源：
ICCS 2010 - INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE, PROCEEDINGS | 2010年 / 1卷 / 01期
关键词：
twisted factorizations; twisted block factorizations; block tridiagonal eigenvalue problem; eigenvector computation; REPRESENTATIONS; IMPLEMENTATION; EIGENVECTOR; ALGORITHM; INVERSE;
D O I：
10.1016/j.procs.2010.04.031
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Non-symmetric and symmetric twisted block factorizations of block tridiagonal matrices are discussed. In contrast to non-blocked factorizations of this type, localized pivoting strategies can be integrated which improves numerical stability without causing any extra fill-in. Moreover, the application of such factorizations for approximating an eigenvector of a block tridiagonal matrix, given an approximation of the corresponding eigenvalue, is outlined. A heuristic strategy for determining a suitable starting vector for the underlying inverse iteration process is proposed. (C) 2010 Published by Elsevier Ltd.
引用
收藏
页码：279 / 287
页数：9
相关论文
共 18 条
  • [1] Block tridiagonalization of "effectively" sparse symmetric matrices
    Bai, YH
    Gansterer, WN
    Ward, RC
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2004, 30 (03): : 326 - 352
  • [2] BISCHOF C, 1994, PROCEEDINGS OF THE SCALABLE HIGH-PERFORMANCE COMPUTING CONFERENCE, P23, DOI 10.1109/SHPCC.1994.296622
  • [3] A framework for symmetric band reduction
    Bischof, CH
    Lang, B
    Sun, XB
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2000, 26 (04): : 581 - 601
  • [4] BUNCH JR, 1977, MATH COMPUT, V31, P163, DOI 10.1090/S0025-5718-1977-0428694-0
  • [5] ACCURATE SINGULAR-VALUES OF BIDIAGONAL MATRICES
    DEMMEL, J
    KAHAN, W
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1990, 11 (05): : 873 - 912
  • [6] The design and implementation of the MRRR algorithm
    Dhillon, Inderjit S.
    Parlett, Beresford N.
    Voemel, Christof
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2006, 32 (04): : 533 - 560
  • [7] Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
    Dhillon, IS
    Parlett, BN
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 387 : 1 - 28
  • [8] On computing an eigenvector of a tridiagonal matrix .1. Basic results
    Fernando, KV
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1997, 18 (04) : 1013 - 1034
  • [9] Computing approximate eigenpairs of symmetric block tridiagonal matrices
    Gansterer, WN
    Ward, RC
    Muller, RP
    Goddard, WA
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2003, 25 (01) : 65 - 85
  • [10] An extension of the divide-and-conquer method for a class of symmetric block-tridiagonal eigenproblems
    Gansterer, WN
    Ward, RC
    Muller, RP
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2002, 28 (01): : 45 - 58
12