Journal of Applied Mathematics and Physics

Volume 7, Issue 9 (September 2019)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.61  Citations  

The LA = U Decomposition Method for Solving Systems of Linear Equations

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DOI: 10.4236/jamp.2019.79140    247 Downloads   682 Views  

ABSTRACT

A method for solving systems of linear equations is presented based on direct decomposition of the coefficient matrix using the form LAX = LB = B’ . Elements of the reducing lower triangular matrix L can be determined using either row wise or column wise operations and are demonstrated to be sums of permutation products of the Gauss pivot row multipliers. These sums of permutation products can be constructed using a tree structure that can be easily memorized or alternatively computed using matrix products. The method requires only storage of the L matrix which is half in size compared to storage of the elements in the LU decomposition. Equivalence of the proposed method with both the Gauss elimination and LU decomposition is also shown in this paper.

Cite this paper

Tiruneh, A. , Debessai, T. , Bwembya, G. and Nkambule, S. (2019) The LA = U Decomposition Method for Solving Systems of Linear Equations. Journal of Applied Mathematics and Physics, 7, 2031-2051. doi: 10.4236/jamp.2019.79140.

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