A Preliminary Study of a Perturbative Approach for the Computation of Matrix Eigenvalues

We consider a new method for the computation of the eigensystem of real symmetric matrices. This method is based on a simple perturbative approach. Given a matrix A we select a matrix A0 close, in some sense, to A and having known eigensystem. Starting from A0 an iterative algorithm considers M matrices Am, m = 1,2,...,M, such that Am is a perturbation of Am−1, and AM = A. Moreover, at each step m = 1,2,...,M, this algorithm computes an approximated eigensystem of Am from an approximated eigensystem of Am−1. We present some preliminary results obtained with this method on some classical test problems.