Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 76, Issue 4, Pages 686-700Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2018.05.010
Keywords
Lanczos version of biconjugate residual (BCR) algorithm; Symmetric solution; General Sylvester matrix equations
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Many problems in control theory can be studied by obtaining the symmetric solution of linear matrix equations. In this investigation, we deal with the symmetric solutions X, Y and Z of the general Sylvester matrix equations {A1XB1 + C1YD1 + E(1)ZF(1) = G(1), A(2)XB(2) + C2YD2 + E(2)ZF(2) = G(2), . . . . . . . . . . . . A(t)XB(t) + CtYDt + E(t)ZE(t) = G(t). The Lanczos version of biconjugate residual (BCR) algorithm is generalized to compute the symmetric solutions of the general Sylvester matrix equations. The convergence properties of this algorithm are discussed and it is proven that it smoothly converges to the symmetric solutions of the general Sylvester matrix equations in a finite number of iterations in the absence of round -off errors. Finally, the comparative numerical results are carried out to support that the current algorithm may be more efficient than other iterative algorithms. (C) 2018 Elsevier Ltd. All rights reserved.
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