^{}Department of Mathematics, Islamic Azad University, Najafabad Branch, Iran.

Abstract

In this paper, a fundamentally new method, based on the denition, is introduced
for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues
of matrices. Some examples are provided to show the accuracy and reliability of the proposed
method. It is shown that the proposed method gives other sequences than that of existing
methods but they still are convergent to the desired eigenvalues, generalized eigenvalues and
quadratic eigenvalues of matrices. These examples show an interesting phenomenon in the
procedure: The diagonal matrix that converges to eigenvalues gives them in decreasing order
in the sense of absolute value. Appendices A to C provide Matlab codes that implement the
proposed algorithms. They show that the proposed algorithms are very easy to program.