COMPUTING SELECTED EIGENVALUES OF SPARSE UNSYMMETRIC MATRICES USING SUBSPACE ITERATION

Authors
Citation
Is. Duff et Ja. Scott, COMPUTING SELECTED EIGENVALUES OF SPARSE UNSYMMETRIC MATRICES USING SUBSPACE ITERATION, ACM transactions on mathematical software, 19(2), 1993, pp. 137-159
Citations number
29
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Sciences",Mathematics
ISSN journal
0098-3500
Volume
19
Issue
2
Year of publication
1993
Pages
137 - 159
Database
ISI
SICI code
0098-3500(1993)19:2<137:CSEOSU>2.0.ZU;2-B
Abstract
This paper discusses the design and development of a code to calculate the eigenvalues of a large sparse real unsymmetric matrix that are th e rightmost, leftmost, or are of largest modulus. A subspace iteration algorithm is used to compute a sequence of sets of vectors that conve rge to an orthonormal basis for the invariant subspace corresponding t o the required eigenvalues. This algorithm is combined with Chebychev acceleration if the rightmost or leftmost eigenvalues are sought, or i f the eigenvalues of largest modulus are known to be the rightmost or leftmost eigenvalues. An option exists for computing the corresponding eigenvectors. The code does not need the matrix explicitly since it o nly requires the user to multiply sets of vectors by the matrix. Sophi sticated and novel iteration controls, stopping criteria, and restart facilities are provided. The code is shown to be efficient and competi tive on a range of test problems.