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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

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Volume 23, Issue 4

Issues

Application of the partitioning method to specific Toeplitz matrices

Predrag Stanimirović / Marko Miladinović / Igor Stojanović / Sladjana Miljković
Published Online: 2013-12-31 | DOI: https://doi.org/10.2478/amcs-2013-0061

Abstract

We propose an adaptation of the partitioning method for determination of theMoore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore-Penrose inverse of specific Toeplitz matrices of an arbitrary size. The method is implemented in MATLAB, and illustrative examples are presented.

Keywords : Moore-Penrose inverse; partitioning method; Toeplitz matrices; MATLAB; image restoration

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About the article

Published Online: 2013-12-31

Published in Print: 2013-12-01


Citation Information: International Journal of Applied Mathematics and Computer Science, Volume 23, Issue 4, Pages 809–821, ISSN (Print) 1641-876X, DOI: https://doi.org/10.2478/amcs-2013-0061.

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