Computing the pseudoinverse of specific Toeplitz matrices using rank-one updates
type: Item
instance of: scholarly article
title: Computing the pseudoinverse of specific Toeplitz matrices using rank-one updates
zbMATH Open document ID: 1400.65018
DOI: 10.1155/2016/9065438
author: Predrag S. Stanimirović
author: Vasilios N. Katsikis
author: Igor Stojanović
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Application of the pure rank-one update algorithm as well as a combination of rank-one updates and the Sherman-Morrison formula in computing the Moore-Penrose inverse of the particular Toeplitz matrix is investigated in the present paper. Such Toeplitz matrices appear in the image restoration process and in many scientific areas that use the convolution. Four different approaches are developed, implemented, and tested on a number of numerical experiments.
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 6953732
Wikidata QID: Q57717603
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9065438
OpenAlex ID: W2507463589
cites work: Q3849175
cites work: A Class of Methods for Solving Nonlinear Simultaneous Equations
cites work: Preconditioning Sparse Nonsymmetric Linear Systems with the Sherman--Morrison Formula
cites work: Q5543004
cites work: The solution of linear systems by using the Sherman-Morrison formula
cites work: AN APPROXIMATE MATRIX INVERSION PROCEDURE BY PARALLELIZATION OF THE SHERMAN–MORRISON FORMULA
cites work: An efficient implementation of the ensemble Kalman filter based on an iterative Sherman-Morrison formula
cites work: Approximate displacement rank and applications
cites work: Solving Toeplitz least squares problems by means of Newton's iteration
cites work: Q3424479
cites work: Modified SMS method for computing outer inverses of Toeplitz matrices
cites work: An Algorithm for the Inversion of Finite Toeplitz Matrices
cites work: Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration
cites work: Q3207128
cites work: The minimum-norm least-squares solution of a linear system and symmetric rank-one updates
cites work: The generalized inverses of perturbed matrices
cites work: Generalized Inversion of Modified Matrices
cites work: Relationships between generalized inverses of a matrix and generalized inverses of its rank-one-modifications
cites work: Computing \(\{2,4\}\) and \(\{2,3\}\)-inverses by using the Sherman-Morrison formula
cites work: Some Applications of the Pseudoinverse of a Matrix
cites work: General forms for the recursive determination of generalized inverses: Unified approach
cites work: Application of the partitioning method to specific Toeplitz matrices
cites work: Applications of the Moore-Penrose inverse in digital image restoration
cites work: Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse
cites work: Q5299431
cites work: Fast computing of the Moore-Penrose inverse matrix
cites work: Deblurring Images
description: scientific article; zbMATH DE number 6953732