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

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DOI: https://doi.org/10.28924/2291-8639-22-2024-103
Published: Jun 24, 2024
Cite as:
I. K. Youssef, Hewayda M. S. Lotfy, Structured Linear Systems and Their Iterative Solutions Through Fuzzy Poisson's Equation, Int. J. Anal. Appl., 22 (2024), 103.

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I. K. Youssef, Hewayda M. S. Lotfy

Abstract

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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