TITLE:
Efficient Generalized Inverse for Solving Simultaneous Linear Equations
AUTHORS:
S. Kadiam Bose, D. T. Nguyen
KEYWORDS:
Generalized Inverse Algorithms, Simultaneous Linear Systems, Matrix Inverse, Singular Matrix, Pseudo Inverse, Cholesky Factorization
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.1,
January
11,
2016
ABSTRACT: Solving large scale system of
Simultaneous Linear Equations (SLE) has been (and continue to be) a major
challenging problem for many real-world engineering and science applications.
Solving SLE with singular coefficient matrices arises from various engineering
and sciences applications [1]-[6]. In this paper, efficient numerical
procedures for finding the generalized (or pseudo) inverse of a general
(square/rectangle, symmetrical/unsymmetrical, non-singular/singular) matrix and
solving systems of Simultaneous Linear Equations (SLE) are formulated and
explained. The developed procedures and its associated computer software (under
MATLAB [7] computer environment) have been based on “special Cholesky
factorization schemes” (for a singular matrix). Test matrices from different
fields of applications have been chosen, tested and compared with other existing
algorithms. The results of the numerical tests have indicated that the
developed procedures are far more efficient than the existing algorithms.