DOI: http://dx.doi.org/10.4314/gjmas.v12i1.3 GLOBAL JOURNAL OF MATHEMATICAL SCIENCES VOL. 11, NO. 1&2, 2012: 21-26 COPYRIGHT© BACHUDO SCIENCE CO. LTD PRINTED IN NIGERIA ISSN 1596-6208 www.globaljournalseries.com, Email: info@globaljournalseries.com ON LU FACTORIZATION ALGORITHM WITH MULTIPLIERS O. E, NTEKIM, I. M. ES UABANA AND U. E. EDEKE 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 n 2 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. KEY WORDS: Lower and Upper Triangular Matrices, Multipliers. INTRODUCTION Let A be a square matrix of order n. An LU factorization or decomposition is a decomposition of the form: A = LU & & & & & & & & & & & .. (1) Where L and U are upper and lower triangular matrices (of the same size) respectively (Horn and Johnson, 1985; Kreyszig, 1993; Morris, 1983; Conte, 1965). The LU factorization is not unique if one only requires that L be lower triangular and U be upper triangular. It is unique if we assign fixed values to the diagonal elements of either L or U (Conte, 1965; Sastry, 1989; Olayi, 2000; Atkinson, 1993). LU decomposition is used for solving system of linear equations, calculating matrix determinants and inverse. THEOREM 1 (EXISTENCE AND UNIQUENESS). The matrix A = (2) admits an LU factorization if and only if all its principal minors are non singular, that is, if a 11 0 0 0 & & 0 (3) (Conte, 1965; Sastry, 1989; Olayi, 2000). LU DECOMPOSITION ALGORITHMS We now outline the various procedures or methods that have hitherto been used to factor a square matrix A into a product of L and U matrices. We assume in all the methods that no interchanges will be necessary. The methods we are going to examine involve writing the general forms of L and U and the unknown elements of L and U are then found by equating corresponding entries in A and LU in a systematic way. 21 O. E, Ntekim, Department of Mathematics/Statistics and Computer Science, University of Calabar, Calaba, Nigeria I. M. Esuabana, Department of Mathemati cs/Statistics, Cross River University of Technology, Calabar, Nigeria U. E. Edeke, Department of Mathematics/Statistics and Computer Science, University of Calabar, Calabar, Nigeria