Open Access
20 May 2003 Direct methods for matrix Sylvester and Lyapunov equations
Danny C. Sorensen, Yunkai Zhou
J. Appl. Math. 2003(6): 277-303 (20 May 2003). DOI: 10.1155/S1110757X03212055


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.


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Danny C. Sorensen. Yunkai Zhou. "Direct methods for matrix Sylvester and Lyapunov equations." J. Appl. Math. 2003 (6) 277 - 303, 20 May 2003.


Published: 20 May 2003
First available in Project Euclid: 26 May 2003

zbMATH: 1028.65039
MathSciNet: MR2036973
Digital Object Identifier: 10.1155/S1110757X03212055

Primary: 15A06 , ‎15A24‎
Secondary: 65F05 , 65F30

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 6 • 20 May 2003
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