The quadratic method for computing the eigenpairs of a martix

Abstract

In this paper we introduce a new method for computing the eigenpairs of a matrix. The quadratic method which has the advantage of working in parallel, is based on solving quadratic nonlinear systems. The starting values of Newton's method used to solve the systems, are obtained by using a homotopy method together with polynomial interpolation. The algorithm is described and several numerical examples are given.

Keywords:

• Matrix
• eigenvalue
• eigenvector
• eigenpair
• homotopy
• symmetric
• non-symmetric

AMS Subject Classifications:

• 65F15
• 65Y05