On Conjugate –Gradient Algorithms

Abstract

The aim of this paper is to recognize the attitude of the conjugate –Gradient Algorithms for solving linear systems Ax=b under the existence of rounding errors. The effect of matrix condition number of A on the relative error of the calculated series of approximations  is analyzed. An especially appealing feature of the algorithm qualified is that error rating can be obtained very easily. Some examples are presented to support the theoretical results and to demonstrate the applicability and efficiency of the methods. The paper ends with some conclusions that sum up the finding of the study. The executed program for calculation is carried using “Matlb7”.