On the Newton's Iterative Method for the Characteristic Equation of a Real Symmetric Matrix

Abstract

The present paper studies the numerical computation of the extreme eigenvalues of a n times n real symmetric matrix A, by the means of the Newton's approximate method for the characteristic polynomial PA(lambda). An iterative algorithm is also presented involving the computation of a trace of an appropriate matrix, instead of using the evaluation of PA(lambda) and its derivative. Numerical examples solved with this algorithm are to be found within as well