Application of the pseudoinverse computation in reconstruction of blurred images

Miljković, Sladjana; Miladinović, Marko; Stanimirović, Predrag S.; Stojanović, Igor

doi:10.2298/fil1203453m

Cited by 12 publications

(4 citation statements)

References 15 publications

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“…The alternative is the use of iterative algorithms to estimate it. In a vast range of fields, such as image and signal processing [1][2][3][4], encryption [5,6], control system analysis [7,8], etc., it is necessary to calculate the inverse or different generalized inverses in order to solve the problems posed.…”

Section: Introductionmentioning

confidence: 99%

Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

et al. 2023

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Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore–Penrose inverse of a singular square matrix or an arbitrary m×n complex matrix. A Kurchatov-type scheme and Steffensen’s method with memory were developed for estimating these types of inverses, improving, in the second case, the order of convergence of the Newton–Schulz scheme. The convergence and its order were studied in the four cases, and their stability was checked as discrete dynamical systems. With large matrices, some numerical examples are presented to confirm the theoretical results and to compare the results obtained with the proposed methods with those provided by other known ones.

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Section: Introductionmentioning

confidence: 99%

Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

et al. 2023

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“…Iterative algorithm is an interesting and very ancient subject (see literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and references therein), due to the importance of the topic in numerical analysis, engineering and applied problems such as economics analysis, physics, dynamical models, and so on. [20][21][22][23] In general, by using a variant of different techniques, such as Taylor series, [24][25][26] decomposition, 4,5,9 quadrature 2,12 and homotopy methods, 13,14 these iterative methods could be derived.…”

Section: Introductionmentioning

confidence: 99%

Fourth-order iterative method without calculating the higher derivatives for nonlinear equation

2019

Journal of Algorithms & Computational Technology

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In this paper, we present firstly several one-step iterative methods including classical Newton's method and Halley's method for root-finding problem based on Thiele's continued fraction. Secondly, by using approximants of the second derivative and the third derivative, we obtain an improved iterative method, which is not only two-step iterative method but also avoids calculating the higher derivatives of the function. Analysis of its convergence shows that the order of convergence of the modified iterative method is four for a simple root of the equation. Finally, to illustrate the efficiency and performance of the proposed method, we give some numerical experiments and comparison.

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“…The Moore-Penrose pseudoinverse arises in many real life applications. It is commonly used in graphics (image recognition [1], image restoration [2], data compression [3]), robotics [4], and statistics [5] as well as diverse branches of engineering [6,7]. Our examination of various algorithms for the pseudoinverse was motivated by the necessity of using such an operation in the local numerical homogenization in solid mechanics.…”

Section: Introductionmentioning

confidence: 99%

On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

Klimczak

Cecot

2019

Mathematical Problems in Engineering

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Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.

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Application of the pseudoinverse computation in reconstruction of blurred images

Cited by 12 publications

References 15 publications

Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

Improving Newton–Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

Fourth-order iterative method without calculating the higher derivatives for nonlinear equation

On Moore‐Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

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