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2021•Advanced Studies Euro-Tbilisi Mathematical JournalRequires access

A splitting iterative method and preconditioner for complex symmetric linear system via real equivalent form

Wenbin Bao, Shu-Xin Miao

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Abstract

In this paper, a splitting iterative method and the corresponding preconditioner are studied for solving a class of complex symmetric linear systems via real equivalent forms. The unconditional convergence theory of the new iterative method is established, and the eigenvalue distribution of the corresponding preconditioned matrix is analyzed. Numerical experiments are given to verify our theoretical results and illustrate effectiveness of the proposed iterative method and the corresponding splitting preconditioner.

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What this paper is about

In this paper, a splitting iterative method and the corresponding preconditioner are studied for solving a class of complex symmetric linear systems via real equivalent forms. The unconditional convergence theory of the new iterative method is established, and the eigenvalue distribution of the corresponding preconditioned matrix is analyzed. Numerical experiments are given to verify our theoretical results and illustrate effectiveness of the proposed iterative method and the corresponding splitting preconditioner.

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Available abstract

In this paper, a splitting iterative method and the corresponding preconditioner are studied for solving a class of complex symmetric linear systems via real equivalent forms. The unconditional convergence theory of the new iterative method is established, and the eigenvalue distribution of the corresponding preconditioned matrix is analyzed. Numerical experiments are given to verify our theoretical results and illustrate effectiveness of the proposed iterative method and the corresponding splitting preconditioner.

Key concepts: Preconditioner, Iterative method, Eigenvalues and eigenvectors, Mathematics, Applied mathematics, Linear system, Convergence (economics), Matrix (chemical analysis)

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