The trace minimization method for the symmetric generalized eigenvalue problem

被引:54
作者
Sameh, A [1 ]
Tong, ZY [1 ]
机构
[1] Purdue Univ, Dept Comp Sci, W Lafayette, IN 47907 USA
基金
美国国家科学基金会;
关键词
trace minimization; Jacobi-Davidson scheme; eigenvalue; eigenvector;
D O I
10.1016/S0377-0427(00)00391-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, the trace minimization method for the generalized symmetric eigenvalue problems proposed by Sameh and Wisniewski [35] is reviewed. Convergence of an inexact trace minimization algorithm is established and a variant of the algorithm that uses expanding subspaces is introduced and compared with the block Jacobi-Davidson algorithm. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 65F15.
引用
收藏
页码:155 / 175
页数:21
相关论文
共 44 条
[1]  
[Anonymous], 1972, International Journal of Numerical Methods in Engineering, DOI [10.1002/nme.1620060207, DOI 10.1002/NME.1620060207]
[2]  
[Anonymous], J REINE ANGEW MATH, DOI DOI 10.1515/CR11.1846.30.51
[3]  
BATHE KJ, 1972, J ENGINEERING MECHAN, V98, P1471
[4]  
BAUER FL, 1957, Z ANGEW MATH PHYS, V8, P214, DOI DOI 10.1007/BF01600502
[5]  
Beckenbach E. F., 1971, INEQUALITIES
[6]  
Clint M., 1970, Computer Journal, V13, P76, DOI 10.1093/comjnl/13.1.76
[7]   THE DAVIDSON METHOD [J].
CROUZEIX, M ;
PHILIPPE, B ;
SADKANE, M .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (01) :62-76
[8]   COMPUTING EIGENVALUES OF VERY LARGE SYMMETRIC-MATRICES - AN IMPLEMENTATION OF A LANCZOS-ALGORITHM WITH NO RE-ORTHOGONALIZATION [J].
CULLUM, J ;
WILLOUGHBY, RA .
JOURNAL OF COMPUTATIONAL PHYSICS, 1981, 44 (02) :329-358
[9]  
CULLUM J, 1979, SPARSE MATRIX P 1978
[10]   REORTHOGONALIZATION AND STABLE ALGORITHMS FOR UPDATING GRAM-SCHMIDT QR FACTORIZATION [J].
DANIEL, JW ;
GRAGG, WB ;
KAUFMAN, L ;
STEWART, GW .
MATHEMATICS OF COMPUTATION, 1976, 30 (136) :772-795