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Optimal preconditioners for systems defined by functions of Toeplitz matrices

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Abstract We propose several circulant preconditioners for systems defined by some functions g of Toeplitz matrices A n . In this paper we are interested in solving g ( A… Click to show full abstract

Abstract We propose several circulant preconditioners for systems defined by some functions g of Toeplitz matrices A n . In this paper we are interested in solving g ( A n ) x = b by the preconditioned conjugate method or the preconditioned minimal residual method, namely in the cases when g ( z ) are the functions e z , sin ⁡ z and cos ⁡ z . Numerical results are given to show the effectiveness of the proposed preconditioners.

Keywords: functions toeplitz; toeplitz matrices; defined functions; preconditioners systems; optimal preconditioners; systems defined

Journal Title: Linear Algebra and its Applications
Year Published: 2018

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