On Lu Factorization Algorithm With Multipliers

Abstract

Various algorithm such as Doolittle, Crouts and Cholesky’s have been proposed to factor a square matrix into a product of L and U matrices, that is, to find L and U such that A = LU; where L and U are lower and upper triangular matrices respectively. These methods are derived by writing the general forms of L and U and the unknown elements of L and U are then formed by equating the corresponding entries in A and LU in a systematic way. This approach for computing L and U for larger values of n will involve many sum of products and will result in n² equations for a matrix of order n. In this paper, we propose a straightforward method based on multipliers derived from modification of Gaussion elimination algorithm.

Keywords: Lower and Upper Triangular Matrices, Multipliers.