#### 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