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BANDED TOEPLITZ PRECONDITIONERS FOR TOEPLITZ MATRICES FROM SINC METHODS 被引量:1
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作者 Zhi-Ru Ren 《Journal of Computational Mathematics》 SCIE CSCD 2012年第5期533-543,共11页
We give general expressions, analyze algebraic properties and derive eigenvalue bounds for a sequence of Toeplitz matrices associated with the sinc discretizations of various orders of differential operators. We demon... We give general expressions, analyze algebraic properties and derive eigenvalue bounds for a sequence of Toeplitz matrices associated with the sinc discretizations of various orders of differential operators. We demonstrate that these Toeplitz matrices can be satisfactorily preconditioned by certain banded Toeplitz matrices through showing that the spectra of the preconditioned matrices are uniformly bounded. In particular, we also derive eigen- value bounds for the banded Toeplitz preconditioners. These results are elementary in constructing high-quality structured preconditioners for the systems of linear equations arising from the sinc discretizations of ordinary and partial differential equations, and are useful in analyzing algebraic properties and deriving eigenvalue bounds for the correspond- ing preconditioned matrices. Numerical examples are given to show effectiveness of the banded Toeplitz preconditioners. 展开更多
关键词 Toeplitz matrix Banded Toeplitz preconditioner Generating function sincmethod Eigenvalue bounds.
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