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Preconditioned GMRES method for a class of Toeplitz linear systems in fractional eigenvalue problems

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Abstract

In this paper, we consider the solution of a class of Toeplitz linear systems coming from the fractional eigenvalue problems. We construct the Strang circulant matrix as a preconditioner to solve the Toeplitz linear systems, and analyze the properties of eigenvalues of the preconditioned coefficient matrix. We also propose the preconditioned generalized minimal residuals method for solving this linear systems, and give the computational costs of this algorithm. The numerical examples show the effecticiency of our method.

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Acknowledgements

We would like to thank the anonymous reviewers for their invaluable comments on an earlier draft of the present manuscript.

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Correspondence to Ying He.

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Communicated by José Tenreiro Machado.

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Zuo, Q., He, Y. Preconditioned GMRES method for a class of Toeplitz linear systems in fractional eigenvalue problems. Comp. Appl. Math. 39, 253 (2020). https://doi.org/10.1007/s40314-020-01258-9

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  • DOI: https://doi.org/10.1007/s40314-020-01258-9

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