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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-andConquer 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 , 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 nonsingular 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.

DIVIDE-AND-CONQUER STRATEGY WITH CHOLESKY'S FACTORIZATION FOR INVERTING SYMMETRIC POSITIVE DEFINITE MATRICES