Relaxation parameters and composite refinement techniques

Meligy, Sh.A.; Youssef, I. K.

doi:10.1016/j.rinam.2022.100282

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…It is revealed that MMSOR runs faster compared with SOR and MSOR. We look forward to considering the effect of refinement techniques [16] and the role of the relaxation parameters [17].…”

Section: Discussionmentioning

confidence: 99%

Structured Linear Systems and Their Iterative Solutions Through Fuzzy Poisson's Equation

Youssef,

Lotfy

2024

Int. J. Anal. Appl.

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A realistic version of the modified successive overrelaxation (MSOR) with four relaxation parameters is introduced (MMSOR) with application to a representative matrix partition. The one-dimensional Poisson’s equation with fuzzy boundary values is the standard source problem for our treatment (it is sufficient to introduce all the concepts in a simple form). The finite difference method with RedBlack (RB)-Labelling of the grid points is used to introduce a fuzzy algebraic system with characterized fuzzy weak solutions (corresponding to black grid points). We introduce the algorithmic structure and the implementation of MMSOR on the de-fuzzified linear system. The choice of relaxation parameters is based on the minimum Spectral Radius (SR) of the iteration matrices. A comparison with SOR (one relaxation parameter) and MSOR (two relaxation parameters) is considered, and a relation between the three methods is revealed. Assuming the same accuracy, the experimental results showed that the MMSOR runs faster than the SOR and the MSOR methods.

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“…It is revealed that MMSOR runs faster compared with SOR and MSOR. We look forward to considering the effect of refinement techniques [16] and the role of the relaxation parameters [17].…”

Section: Discussionmentioning

confidence: 99%

Structured Linear Systems and Their Iterative Solutions Through Fuzzy Poisson's Equation

Youssef,

Lotfy

2024

Int. J. Anal. Appl.

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“…A special class is represented by systems of linear algebraic equations with symmetric positive definite matrices. Depending on the proposed approach to constructing the next iterative approximation, several iterative methods for solving these SLAE are distinguished [1][2][3]. Among them are the methods of Seidel and Successive OverRelaxation.…”

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confidence: 99%

Symmetrized Versions of the Seidel and Successive OverRelaxation Methods for Solving Two-Dimensional Difference Problems of Elliptic Type

Sidoryakina,

Solomakha

2023

CMIT

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Introduction. This article is devoted to the consideration of options for symmetrization of two-layer implicit iterative methods for solving grid equations that arise when approximating boundary value problems for two-dimensional elliptic equations. These equations are included in the formulation of many problems of hydrodynamics, hydrobiology of aquatic systems, etc. Grid equations for these problems are characterized by a large number of unknowns — from 106 to 1010, which leads to poor conditionality of the corresponding system of algebraic equations and, as a consequence, to a significant increase in the number of iterations, necessary to achieve the specified accuracy. The article discusses a method for reducing the number of iterations for relatively simple methods for solving grid equations, based on the procedure of symmetrized traversal of the grid region.Materials and Methods. The methods for solving grid equations discussed in the article are based on the procedure of symmetrized traversal along the rows (or columns) of the grid area.Results. Numerical experiments have been performed for a model problem — the Dirichlet difference problem for the Poisson equation, which demonstrate a reduction in the number of iterations compared to the basic algorithms of these methods.Discussion and Conclusions. This work has practical significance. The developed software allows it to be used to solve specific physical problems, including as an element of a software package.

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An Accelerated Iterative Technique: Third Refinement of Gauss–Seidel Algorithm for Linear Systems

Audu,

Essien

2023

Iocma 2023

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Relaxation parameters and composite refinement techniques

Cited by 4 publications

References 17 publications

Structured Linear Systems and Their Iterative Solutions Through Fuzzy Poisson's Equation

Structured Linear Systems and Their Iterative Solutions Through Fuzzy Poisson's Equation

Symmetrized Versions of the Seidel and Successive OverRelaxation Methods for Solving Two-Dimensional Difference Problems of Elliptic Type

An Accelerated Iterative Technique: Third Refinement of Gauss–Seidel Algorithm for Linear Systems

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