학술논문
A fast numerical method for block lower triangular Toeplitz with dense Toeplitz blocks system with applications to time-space fractional diffusion equations.
Document Type
Article
Author
Source
Subject
*TOEPLITZ matrices
*BLOCKS (Group theory)
*HEAT equation
*FRACTIONAL calculus
*REPRESENTATION theory
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Language
ISSN
1017-1398
Abstract
Based on the circulant-and-skew-circulant representation of Toeplitz matrix inversion and the divide-and-conquer technique, a fast numerical method is developed for solving N-by- N block lower triangular Toeplitz with M-by- M dense Toeplitz blocks system with $\mathcal {O}(MN\log N(\log N+\log M))$ complexity and $\mathcal {O}(NM)$ storage. Moreover, the method is employed for solving the linear system that arises from compact finite difference scheme for time-space fractional diffusion equations with significant speedup. Numerical examples are given to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]