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ACM Transactions on Mathematical Software (TOMS), Volume 28 Issue 4, December 2002

Implementing Hager's exchange methods for matrix profile reduction
John K. Reid, Jennifer A. Scott
Pages: 377-391
DOI: 10.1145/592843.592844
Hager recently introduced down and up exchange methods for reducing the profile of a sparse matrix with a symmetric sparsity pattern. The methods are particularly useful for refining orderings that have been obtained using a standard profile...

Recursive blocked algorithms for solving triangular systems—Part I: one-sided and coupled Sylvester-type matrix equations
Isak Jonsson, Bo Kågström
Pages: 392-415
DOI: 10.1145/592843.592845
Triangular matrix equations appear naturally in estimating the condition numbers of matrix equations and different eigenspace computations, including block-diagonalization of matrices and matrix pairs and computation of functions of matrices. To...

Recursive blocked algorithms for solving triangular systems—Part II: two-sided and generalized Sylvester and Lyapunov matrix equations
Isak Jonsson, Bo Kågström
Pages: 416-435
DOI: 10.1145/592843.592846
We continue our study of high-performance algorithms for solving triangular matrix equations. They appear naturally in different condition estimation problems for matrix equations and various eigenspace computations, and as reduced systems in...

Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions
Amparo Gil, Javier Segura, Nico M. Temme
Pages: 436-447
DOI: 10.1145/592843.592847
Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments Gi(z), Hi(z), and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series, and asymptotic expansions. For...

A software package for sparse orthogonal factorization and updating
Ove Edlund
Pages: 448-482
DOI: 10.1145/592843.592848
Although there is good software for sparse QR factorization, there is little support for updating and downdating, something that is absolutely essential in some linear programming algorithms, for example. This article describes an implementation of...