Algorithm 705; a FORTRAN-77 software package for solving the Sylvester matrix equation AXBT + CXDT = E

Authors:
Judith D. Gardiner;Matthew R. Wette;Alan J. Laub;James J. Amato;Cleve B. Moler
Affiliations:
-;-;-;-;-
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1992

Citing 1
Cited 7

Solution of the Sylvester matrix equation AXBT + CXDT = E

ACM Transactions on Mathematical Software (TOMS)

Solution of the Sylvester matrix equation AXBT + CXDT = E

ACM Transactions on Mathematical Software (TOMS)
LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs

ACM Transactions on Mathematical Software (TOMS)
Remark on algorithm 705: A Fortran-77 software package for solving the Sylvester matrix equation AXBT + CXDT = E

ACM Transactions on Mathematical Software (TOMS)
Recursive blocked algorithms for solving triangular systems—Part I: one-sided and coupled Sylvester-type matrix equations

ACM Transactions on Mathematical Software (TOMS)
Recursive blocked algorithms for solving triangular systems—Part II: two-sided and generalized Sylvester and Lyapunov matrix equations

ACM Transactions on Mathematical Software (TOMS)
Parallel Two-Sided Sylvester-Type Matrix Equation Solvers for SMP Systems Using Recursive Blocking

PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
On the numerical solution of large-scale sparse discrete-time Riccati equations

Advances in Computational Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper documents a software package for solving the Sylvester matrix equation (1) AXBT + CXDT = e All quantities are real matrices; A and C are m x n; B and D are m x n; and X and E are m x n. The unknown is X. Two symmetric forms of Eq. (1) are treated separately for efficiency. They are the continuous-time symmetric Sylvester equation (2) AXET + EXAT + C = 0 and the discrete time equation (3) AXAT + C = 0, for which A, E, and C is symmetric. The software also provides a means for estimating the condition number of these three equations. The algorithms employed are more fully described in an accompanying paper [3].