Convergence of Triple Accelerated Over-Relaxation (TAOR) Method for M-Matrix Linear Systems

Subject Areas : Numerical Analysis

Khadeejah Audu ¹ , Yusuph Yahaya ² , Rufus Adeboye ³ , Usman Abubakar ⁴

1 - Department of Mathematics, School of Physical Sciences, Federal University of Technology, Minna, Nigeria
2 - Department of Mathematics, School of Physical Sciences, Federal University of Technology, Minna, Nigeria
3 - Department of Mathematics, School of Physical Sciences, Federal University of Technology, Minna, Nigeria
4 - Department of Mathematics, School of Physical Sciences, Federal University of Technology, Minna, Nigeria

Received: 2021-02-04 Accepted : 2021-09-19 Published : 2021-06-01

Keywords: TAOR Method, $ M- $matrix, Linear systems, Spectral Radius, Convergence Conditions,

Abstract :

In this paper, we propose some necessary conditions for convergence of Triple Accelerated Over-Relaxation (TAOR) method with respect to $M-$ coefficient matrices. The theoretical approach for the proofs is analyzed through some standard procedures in the literature. Some numerical experiments are performed to show the efficiency of our approach, and the results obtained compared favourably with those obtained through the existing methods in terms of spectral radii of their iteration matrices.

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