Pre-Numerical Tests for a New Conjugate Gradient Method

Abstract

The performance of a new beta in conjugate gradient method is generally measured on its CPU time and the number of iterations using large scale problems without concerning the accuracy of the solution attained. The method is claimed to be the best when less CPU time is used in comparison with the other classical beta. However, the accuracy of the solution gained compared to the exact solution of the function has never been tested as part of the performance measurement. Our previous research has already proven that our new beta perform well in both speed and number of iterations used. Therefore, in this research, we will accommodate this with alternative numerical test on the new beta in assessing the accuracy of the gained solution. This is to further ensure the efficiency of the new beta. Assessment was done with four other classical conjugate gradient methods on fourteen small scale problems. Results attained were promising to be tested for more tests in real functional problems.