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TitleTrigonometric transform splitting methods for real symmetric Toeplitz systems
Author(s)Zhongyun Liu
Nianci Wu
Xiaorong Qin
Zhang, Yulin
KeywordsSine transform
Cosine transform
Matrix splitting Iterative methods
Real Toeplitz matrices
Iterative methods
Matrix splitting
Issue date2018
JournalComputers and Mathematics With Applications
Abstract(s)In this paper, we study efficient iterative methods for real symmetric Toeplitz systems based on the trigonometric transformation splitting (TTS) of the real symmetric Toeplitz matrix A. Theoretical analyses show that if the generating function f of the n × n Toeplitz matrix A is a real positive even function, then the TTS iterative methods converge to the unique solution of the linear system of equations for sufficient large n. Moreover, we derive an upper bound of the contraction factor of the TTS iteration which is dependent solely on the spectra of the two TTS matrices involved. Different from the CSCS iterative method in Ng (2003) in which all operations counts concern complex operations when the DFTs are employed, even if the Toeplitz matrix A is real and symmetric, our method only involves real arithmetics when the DCTs and DSTs are used. The numerical experiments show that our method works better than CSCS iterative method and much better than the positive definite and skew-symmetric splitting (PSS) iterative method in Bai et al. (2005) and the symmetric Gauss–Seidel (SGS) iterative method.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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