Improving tcuracy of the eigenvalues of eigenvalue problem by graeffe-newton-raphson method

Abstract

The direct way of finding the eigenvalues of Eigenvalue problems is to find the roots of the characteristic polynomial of the resultant matrix (arising from the discrtization of the eigenvalue problem) and the results are always inaccurate due to ill conditioning. Hence, it is proposed here that the result of the Graeffe’s root squaring method for finding the roots of a polynomial could be improved by applying the Newton-Raphson method to give a result to any desired accuracy of any Eigenvalue problem.

Keywords: Graeffe’s method, Newtons-Raphson approximation, differential transform, Eigenvalue