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Practical RPCG methods for complex symmetric linear systems

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Abstract

We investigate the restrictively preconditioned conjugate gradient (RPCG) method for complex symmetric linear systems. First, we transform the complex symmetric linear system into an equivalent block two-by-two linear system. Then, by making full use of the real and imaginary parts of the coefficient matrix, we construct a restrictive preconditioner with a parameter and propose a practical RPCG method for solving the complex symmetric linear systems. Finally, we analyze the spectral properties of the preconditioned matrix and give a formula for estimating the parameter. In numerical experiments, we use two examples to demonstrate the robustness and effectiveness of the practical RPCG method for solving the complex symmetric linear systems.

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Shu-Ru He & Fang Chen

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  1. Shu-Ru He
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  2. Fang Chen
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Correspondence to Fang Chen.

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Supported by R &D Program of Beijing Municipal Education Commission (No. KM202011232019), P.R. China.

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He, SR., Chen, F. Practical RPCG methods for complex symmetric linear systems. Comp. Appl. Math. 42, 264 (2023). https://doi.org/10.1007/s40314-023-02412-9

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  • DOI: https://doi.org/10.1007/s40314-023-02412-9

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