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Mathematics 2019, 7(1), 105; https://doi.org/10.3390/math7010105

The Four-Parameter PSS Method for Solving the Sylvester Equation

Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China
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Received: 16 November 2018 / Revised: 20 December 2018 / Accepted: 26 December 2018 / Published: 20 January 2019
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Abstract

In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter’s value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime. View Full-Text
Keywords: Sylvester equation; Positive and skew-Hermitian iterative method; FPPSS iterative method Sylvester equation; Positive and skew-Hermitian iterative method; FPPSS iterative method
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 (CC BY 4.0).
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Shen, H.-L.; Li, Y.-R.; Shao, X.-H. The Four-Parameter PSS Method for Solving the Sylvester Equation. Mathematics 2019, 7, 105.

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