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.

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

EGIDI, Nadaniela;MAPONI, Pierluigi
2014-01-01

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/388058
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