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Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations
Lu X.1; Pang H.-K.2; Sun H.-W.1
2015
Source PublicationNumerical Linear Algebra with Applications
ISSN10991506 10705325
Volume22Issue:5Pages:866-882
Abstract

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{lunate}-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.

KeywordBlock Triangular Toeplitz Matrix Block ε{Lunate}-circulant Matrix Fourier Transform Fractional Sub-diffusion Equations
DOIhttps://doi.org/10.1002/nla.1972
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000360768900006
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Citation statistics
Cited Times [WOS]:16   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Department of Mathematics, University of Macau, Macau, China
2.School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lu X.,Pang H.-K.,Sun H.-W.. Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations[J]. Numerical Linear Algebra with Applications,2015,22(5):866-882.
APA Lu X.,Pang H.-K.,&Sun H.-W..(2015).Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations.Numerical Linear Algebra with Applications,22(5),866-882.
MLA Lu X.,et al."Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub-diffusion equations".Numerical Linear Algebra with Applications 22.5(2015):866-882.
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