Comparative study of Symmetric Gauss-Seidel methods and preconditioned Symmetric Gauss-Seidel methods for linear system

Nirupma Bhatti; Niketa

doi:10.30574/ijsra.2023.8.1.0155

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Comparative study of Symmetric Gauss-Seidel methods and preconditioned Symmetric Gauss-Seidel methods for linear system

Nirupma Bhatti ^*and Niketa

Department of Mathematics, IIHS, Kurukshetra University, Haryana, India.

Research Article

International Journal of Science and Research Archive, 2023, 08(01), 940–947.

Article DOI: 10.30574/ijsra.2023.8.1.0155

DOI url: https://doi.org/10.30574/ijsra.2023.8.1.0155

Publication history

Received on 01 January 2023; revised on 14 February 2023; accepted on 17 February 2023

Abstract

This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New Symmetric Gauss-Seidel (NSGS), and Parametric Symmetric Gauss-Seidel (PSGS) methods for solving the linear system Ax = b are considered. This system is preconditioned with precondition type I + S. Convergence properties are analyzed with standard procedures and a numerical experiment is undertaken to compare the efficiency of the matrix. Algorithms are prepared. MATLAB software is used for checking computational efficiency of preconditioned iterative methods. Results indicate the effectiveness of preconditioning.

Keywords

Symmetric Gauss-Seidel (SGS) method; New Symmetric Gauss-Seidel (NSGS) method; Parametric Symmetric Gauss-Seidel (PSGS) method; Condition number; Spectral radius

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How to cite this article

Nirupma Bhatti and Niketa. Comparative study of Symmetric Gauss-Seidel methods and preconditioned Symmetric Gauss-Seidel methods for linear system. International Journal of Science and Research Archive, 2023, 08(01), 940–947. Article DOI: https://doi.org/10.30574/ijsra.2023.8.1.0155

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