Solving large system of linear equation using successive 0ver‐relaxation, conjugate gradient and preconditioned conjugate gradient
Abstract
System of linear equations is widely used especially in industries. Industrial mathematical
applications usually involve large problem. System of linear equation can be solved using
direct and indirect method. Direct method requires the use of inverse matrix to solve the
problem. However, for large system of linear equation, finding an inverse could be difficult
and time consuming. Therefore, indirect methods in the form of numerical calculation
such as Successive Over‐Relaxation, Conjugate Gradient and Preconditioned Conjugate
Gradient are used. The aim of this research is to compare the performance of those three
methods to solve variety of system of linear equation from small scale to large scale in
term of number of iteration and CPU time. Numerical results show that the Conjugate
Gradient method is the best method for solving system of linear equation in terms of both
number of iteration and CPU time. Above all, those three methods could be used to solve
system of linear equations.