SOME APPLICATION OF IDEALS OF AG-RING
Thiti Gaketem · International Electronic Journal of Pure and Applied Mathematics · 2014
In this paper we study the solution of a system of equations Ax=b with singular and nearly singular, symmetric positive definite coefficient matrix A. Our algorithm based on, the Divide and Conquer strategy leading to the Divide-and-Conquer Algorithm (D&C algorithm) with, Cholesky's factorization algorithm.The Cholesky's factorization will be used to convert the matrix into a product of the form LL T , where L is a lower triangular matrix.The algorithm will be implemented on MATLAB and simulated as a user-subroutine.The user-subroutine is considering MATLAB features for reducing the round-off error especially for sensitive systems.Numerical examples will be given of a non-singular matrix and another for illconditioned matrix.The effect of round-off error will be analyzed.Results will be compared with previous ones, where LU factorization is used.