A New Improved Classical Iterative Algorithm for Solving System of Linear Equations

Muhammad Shakeel Rind Baloch; Zubair Ahmed Kalhoro; Mir Sarfraz Khalil; Prof.
Prof. Abdul Wasim Shaikh

Author(s)

Muhammad Shakeel Rind Baloch Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Pakistan

Zubair Ahmed Kalhoro Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Pakistan

Mir Sarfraz Khalil Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Pakistan

Prof. Prof. Abdul Wasim Shaikh Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Pakistan

Abstract

The fundamental problem of linear algebra is to solve the system of linear equations (SOLE’s). To solve SOLE’s, is one of the most crucial topics in iterative methods. The SOLE’s occurs throughout the natural sciences, social sciences, engineering, medicine and business. For the most part, iterative methods are used for solving sparse SOLE’s. In this research, an improved iterative scheme namely, ‘’a new improved classical iterative algorithm (NICA)’’ has been developed. The proposed iterative method is valid when the co-efficient matrix of SOLE’s is strictly diagonally dominant (SDD), irreducibly diagonally dominant (IDD), M-matrix, Symmetric positive definite with some conditions and H-matrix. Such types of SOLE’s does arise usually from ordinary differential equations (ODE’s) and partial differential equations (PDE’s). The proposed method reduces the number of iterations, decreases spectral radius and increases the rate of convergence. Some numerical examples are utilized to demonstrate the effectiveness of NICA over Jacobi (J), Gauss Siedel (GS), Successive Over Relaxation (SOR), Refinement of Jacobi (RJ), Second Refinement of Jacobi (SRJ), Generalised Jacobi (GJ) and Refinement of Generalised Jacobi (RGJ) methods.

Publication Details

Page(s) 69-81

DOI DOI not available

Published Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 58, Issue: 4, Year: 2021

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Keywords

Diagonally Dominant, Diagonally Dominant, Diagonally Dominant, Diagonally Dominant, Diagonally Dominant, Diagonally Dominant, Diagonally Dominant, Diagonally Dominant, M-matrix, M-matrix, M-matrix, M-matrix, Rate of Convergence., Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, Irreducibly Diagonally Dominant, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, H-matrix, M-matrix, M-matrix, M-matrix, M-matrix, M-matrix, M-matrix, M-matrix, M-matrix, M-matrix, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Refinement Jacobi, Generalized Jacobi