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A direct method for solving block‐Toeplitz with near‐circulant‐block systems with applications to hybrid manufacturing systems
Authors:Wai‐Ki Ching  Michael K Ng  Wai‐On Yuen
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. Copyright © 2005 John Wiley & Sons, Ltd.
Keywords:Sherman–  Morrison–  Woodbury formula  Toeplitz matrix  circulant matrix  re‐manufacturing systems  steady‐state probability distribution
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