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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 standard algorithms. Building on our successful...
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 sparse LQ factorization, including block...
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 solve a triangular matrix equation is also a major...
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 reduction algorithm, such as the Sloan method. The...
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 real z , comparison with a previous code by A. J. MacLeod...
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