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Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub‐diffusion equations
Author(s) -
Lu Xin,
Pang HongKui,
Sun HaiWei
Publication year - 2015
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1972
Subject(s) - toeplitz matrix , circulant matrix , mathematics , block matrix , triangular matrix , band matrix , dft matrix , discretization , matrix (chemical analysis) , inversion (geology) , square matrix , mathematical analysis , algorithm , symmetric matrix , eigenvalues and eigenvectors , invertible matrix , pure mathematics , paleontology , physics , materials science , quantum mechanics , composite material , structural basin , biology
Summary A fast approximate inversion method is proposed for the block lower triangular Toeplitz with tri‐diagonal blocks (BL3TB) matrix. The BL3TB matrix is approximated by a block ϵ ‐circulant matrix, which can be efficiently inverted using the fast Fourier transforms. The error estimation is given to show the high accuracy of the approximation. In applications, the proposed method is employed to solve the fractional sub‐diffusion equation whose discretized matrix by a finite difference method is a BL3TB matrix. Numerical experiments are carried out to demonstrate the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.