Application of the partitioning method to specific Toeplitz matrices

Predrag Stanimirović; Marko Miladinović; Igor Stojanović; Sladjana Miljković

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 4, page 809-821
  • ISSN: 1641-876X

Abstract

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We propose an adaptation of the partitioning method for determination of the Moore-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.

How to cite

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Predrag Stanimirović, et al. "Application of the partitioning method to specific Toeplitz matrices." International Journal of Applied Mathematics and Computer Science 23.4 (2013): 809-821. <http://eudml.org/doc/262291>.

@article{PredragStanimirović2013,
abstract = {We propose an adaptation of the partitioning method for determination of the Moore-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.},
author = {Predrag Stanimirović, Marko Miladinović, Igor Stojanović, Sladjana Miljković},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Moore-Penrose inverse; partitioning method; Toeplitz matrices; MATLAB; image restoration; MATLAB; numerical examples; convolution kernel},
language = {eng},
number = {4},
pages = {809-821},
title = {Application of the partitioning method to specific Toeplitz matrices},
url = {http://eudml.org/doc/262291},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Predrag Stanimirović
AU - Marko Miladinović
AU - Igor Stojanović
AU - Sladjana Miljković
TI - Application of the partitioning method to specific Toeplitz matrices
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 4
SP - 809
EP - 821
AB - We propose an adaptation of the partitioning method for determination of the Moore-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.
LA - eng
KW - Moore-Penrose inverse; partitioning method; Toeplitz matrices; MATLAB; image restoration; MATLAB; numerical examples; convolution kernel
UR - http://eudml.org/doc/262291
ER -

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