Convergence Results of the Biconjugate Residual Algorithm for Solving Generalized Sylvester Matrix Equation |
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| Authors: | Masoud Hajarian |
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| Affiliation: | Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran |
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| Abstract: | In this article, we investigate a variant of the biconjugate residual (BCR) algorithm to solve the generalized Sylvester matrix equation  which includes the well‐known Lyapunov, Stein and Sylvester matrix equations. We show that the BCR algorithm with any (special) initial matrix pair can smoothly compute the (least Frobenius norm) solution pair of the generalized Sylvester matrix equation within a finite number of iterations in the absence of round‐off errors. Finally the accuracy and effectiveness of the BCR algorithm in comparison to some existing algorithms are demonstrated by two numerical examples. |
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| Keywords: | Biconjugate residual algorithm finite number of iterations generalized Sylvester matrix equation |
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which includes the well‐known Lyapunov, Stein and Sylvester matrix equations. We show that the BCR algorithm with any (special) initial matrix pair can smoothly compute the (least Frobenius norm) solution pair of the generalized Sylvester matrix equation within a finite number of iterations in the absence of round‐off errors. Finally the accuracy and effectiveness of the BCR algorithm in comparison to some existing algorithms are demonstrated by two numerical examples.