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

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...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 39; no. 4
Main Authors Zuo, Qian, He, Ying
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2020
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Eigenvalues
Linear systems
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix
Matrix methods
Strang circulant matrix
GMRES
Precondition
93C15
Toeplitz linear systems
65F18
Fractional eigenvalue problems
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Summary: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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-020-01258-9