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A direct method for solving block‐Toeplitz with near‐circulant‐block systems with applications to hybrid manufacturing systems
Author(s) -
Ching WaiKi,
Ng Michael K.,
Yuen WaiOn
Publication year - 2005
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.430
Subject(s) - toeplitz matrix , circulant matrix , block (permutation group theory) , fast fourier transform , mathematics , matrix (chemical analysis) , algorithm , linear system , process (computing) , computer science , combinatorics , pure mathematics , mathematical analysis , materials science , composite material , operating system
In this paper, we present a direct method for solving linear systems of a block‐Toeplitz matrix with each block being a near‐circulant matrix. The direct method is based on the fast Fourier transform (FFT) and the Sherman–Morrison–Woodbury formula. We give a cost analysis for the proposed method. The method is then applied to solve the steady‐state probability distribution of a hybrid manufacturing system which consists of a manufacturing process and a re‐manufacturing process. Copyright © 2005 John Wiley & Sons, Ltd.