期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 50, 期 5-6, 页码 741-752出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2005.03.011
关键词
Toeplitz matrix; fast algorithm; direct inversion
We propose a fast algorithm for the construction of a data-sparse inverse of a general Toeplitz matrix. The computational cost for inverting an N x N Toeplitz matrix equals the cost of four length-N FFTs plus an O(N)-term. This cost should be compared to the O(N log(2) N) cost of previously published methods. Moreover, while those earlier methods are based on algebraic considerations, the procedure of this paper is analysis-based; as a result, its stability does not depend on the symmetry and positive-definiteness of the matrix being inverted. The performance of the scheme is illustrated with numerical examples. (c) 2005 Elsevier Ltd. All rights reserved.
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