Divide-and-Conquer Strategy with LU Factorization for Inverting Symmetric Positive Definite Matrices

Abstract

We studied 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, LU Factorization algorithm. The LU Factorization was used to convert the matrix into a product of the form LU, where L is a lower triangular matrix and U is upper triangular matrix. The algorithm was been 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 was given of a non- singular matrix and another for ill-conditioned matrix. The effect of round-off error was analyzed. We compared results with previous ones, where LU factorization is used.