Name
Title | ||
|---|---|---|
Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration |
Abstract | ||
|---|---|---|
This paper discusses the design and development of a code to calculate the eigenvalues of a large sparse real unsymmetric matrix that are the rightmost, leftmost, or are of the largest modulus. A subspace iteration algorithm is used to compute a sequence of sets of vectors that converge to an orthonormal basis for the invariant subspace corresponding to the required eigenvalues. This algorithm is combined with Chebychev acceleration if the rightmost or leftmost eigenvalues are sought, or if 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 only requires the user to multiply sets of vectors by the matrix. Sophisticated and novel iteration controls, stopping criteria, and restart facilities are provided. The code is shown to be efficient and competitive on a range of test problems. |
Year | DOI | Venue |
|---|---|---|
1993 | 10.1145/152613.152614 | ACM Trans. Math. Softw. |
Keywords | Field | DocType |
eigenvectors,subspace iteration algorithm,required eigenvalues,sparse unsymmetric,orthonormal basis,large sparse matrices,largest modulus,eigenvalues,subspace iteration,real unsymmetric matrices,test problem,novel iteration control,leftmost eigenvalues,corresponding eigenvectors,large sparse real unsymmetric,chebychev acceleration,sparse matrices,iterative algorithm | Mathematical optimization,Subspace topology,Matrix (mathematics),Invariant subspace,Spectrum of a matrix,Orthonormal basis,Acceleration,Code (cryptography),Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
19 | 2 | 0098-3500 |
Citations | PageRank | References |
9 | 3.31 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| I. S. Duff | 1 | 1575 | 530.95 |
| J. A. Scott | 2 | 9 | 3.31 |