ABSTRACT
The Gaussian elimination is an intuitively appealing method for solving a matrix.
However, there is a more efficient and preferred direct method called LU
decomposition. The Gaussian elimination is made up of two stages: forward
elimination, and back substitution. Tests have shown that it is the first stage, the
forward elimination, that takes most of the computational effort. For 10 equations it
represents approximately 80% of the total work and for more than 20 equations it is
over 90%. By 100 equation systems it represents virtually 100% of the total effort.
Any improvement in the method, therefore, must concentrate on this first step as
the substitution steps are relatively cheap. One such method is lower upper (LU)
decomposition, which involves three stages:
