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ACM Transactions on Mathematical Software (TOMS), Volume 19 Issue 2, June 1993

Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration
I. S. Duff, J. A. Scott
Pages: 137-159
DOI: 10.1145/152613.152614
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...

The generalized Schur decomposition of an arbitrary pencil A–&lgr;B—robust software with error bounds and applications. Part I: theory and algorithms
James Demmel, Bo Kågström
Pages: 160-174
DOI: 10.1145/152613.152615
Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil A – &lgr;B (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of A –...

The generalized Schur decomposition of an arbitrary pencil A–&lgr;B—robust software with error bounds and applications. Part II: software and applications
James Demmel, Bo Kågström
Pages: 175-201
DOI: 10.1145/152613.152616
Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil A – &lgr;B (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of A –...

On computing condition numbers for the nonsymmetric eigenproblem
Z. Bai, James Demmel, A. McKenney
Pages: 202-223
DOI: 10.1145/152613.152617
We review the theory of condition numbers for the nonsymmetric eigenproblem and give a tabular summary of bounds for eigenvalues, means of clusters of eigenvalues, eigenvectors, invariant subspaces, and related quantities. We describe the design...

Algorithm 718: A FORTRAN subroutine to solve the eigenvalue allocation problem for single-input systems
George Miminis, Michael Reid
Pages: 224-232
DOI: 10.1145/152613.152618
An efficient implementation of an algorithm for the eigenvalue allocation (pole placement) problem of single-input linear systems using state feedback is given in this paper. The implementation uses the BLAS level-1 [2] subroutines when possible...

Enhancements of ANALYZE: a computer-assisted analysis system for linear programming
Harvey J. Greenberg
Pages: 233-256
DOI: 10.1145/152613.152619
This describes enhancements to provide more advanced computer-assisted analysis of instances of linear programming models. Three categories of enhancements are described: views, engines for obtaining information, and rule-based advising....

Generating a sample from a k-cell table with changing probabilities in O(log2k time
George S. Fishman, L. Stephen Yarberry
Pages: 257-261
DOI: 10.1145/152613.152621