Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 245057 |

Danny C. Sorensen, Yunkai Zhou, "Direct methods for matrix Sylvester and Lyapunov equations", Journal of Applied Mathematics, vol. 2003, Article ID 245057, 27 pages, 2003.

Direct methods for matrix Sylvester and Lyapunov equations

Received12 Dec 2002
Revised31 Jan 2003


We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels-Stewart method for A1X+XA2+D=0 and Hammarling's method for AX+XAT+BBT=0 with A stable. We construct three schemes for solving the unitarily reduced quasitriangular systems. We also construct a new rank-1 updating scheme in Hammarling's method. This new scheme is able to accommodate a B with more columns than rows as well as the usual case of a B with more rows than columns, while Hammarling's original scheme needs to separate these two cases. We compared all of our schemes with the Matlab Sylvester and Lyapunov solver lyap.m; the results show that our schemes are much more efficient. We also compare our schemes with the Lyapunov solver sllyap in the currently possibly the most efficient control library package SLICOT; numerical results show our scheme to be competitive.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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