Browsing by Author "Adeboye, K. R."

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    EXTENDED ACCELERATED OVER-RELAXATION (EAOR) METHOD FOR SOLUTION OF A LARGE AND SPARSELINEAR SYSTEMS
    (Federal University of Technology, Minna, Nigeria, 2021-06-14) Khadeejah James Audu; Yahaya, Y. A.; Adeboye, K. R.; Abubakar, U. Y.
    In this research, we introduce a stationary iterative method called Extended Accelerated Over Relaxation (EAOR) method for solving linear systems. The method, an extension of the Accelerated Over Relaxation (A OR) method, was derived through the interpolation procedure with respect to the sub-matrices in application of a genera/ linear stationary schemes. We studied the convergence properties of the method for special matrices such as L-, H- and irreducible diagonally dominant matrices and proposed some convergence theorems. Some numerical tests were carried out to test the efficiency of the proposed method with existing methods in terms of number of iterations, spectral radius and computational time. The results revealed the superiority of the proposed EAOR method over the AOR method in terms of convergence rate.
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    Refinement of Extended Accelerated Over Relaxation method for solution of linear systems.
    (Benue State University, Makurdi, Nigeria, 2021-09-22) Khadeejah James Audu; Yahaya, Y. A.; Adeboye, K. R.; Abubakar, U. Y.
    Given any linear stationary iterative methods in the form 𝑧(𝑖+1) = 𝐽𝑧(𝑖) + 𝑓, where 𝐽 is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form 𝐴𝑧 = 𝑏. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.