A direct method for solving block-Toeplitz with near-circulant-block systems with applications to hybrid manufacturing systems

Wai Ki Ching; Kwok Po NG; Wai On Yuen

doi:10.1002/nla.430

A direct method for solving block-Toeplitz with near-circulant-block systems with applications to hybrid manufacturing systems

Wai Ki Ching, Kwok Po NG^*, Wai On Yuen

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	957-966
Number of pages	10
Journal	Numerical Linear Algebra with Applications
Volume	12
Issue number	10
DOIs	https://doi.org/10.1002/nla.430
Publication status	Published - Dec 2005

User-Defined Keywords

Circulant matrix
Re-manufacturing systems
Sherman-Morrison-Woodbury formula
Steady-state probability distribution
Toeplitz matrix

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10.1002/nla.430

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title = "A direct method for solving block-Toeplitz with near-circulant-block systems with applications to hybrid manufacturing systems",

abstract = "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.",

keywords = "Circulant matrix, Re-manufacturing systems, Sherman-Morrison-Woodbury formula, Steady-state probability distribution, Toeplitz matrix",

author = "Ching, {Wai Ki} and NG, {Kwok Po} and Yuen, {Wai On}",

year = "2005",

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AU - Ching, Wai Ki

AU - NG, Kwok Po

AU - Yuen, Wai On

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Y1 - 2005/12

N2 - 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.

AB - 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.

KW - Circulant matrix

KW - Re-manufacturing systems

KW - Sherman-Morrison-Woodbury formula

KW - Steady-state probability distribution

KW - Toeplitz matrix

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JF - Numerical Linear Algebra with Applications

IS - 10

ER -

A direct method for solving block-Toeplitz with near-circulant-block systems with applications to hybrid manufacturing systems

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