A mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices

Subject Areas : History and biography

M. Nili Ahmadabadi ¹ (Department of Mathematics, Islamic Azad University, Najafabad Branch, Iran)

Received: 2012-01-01 Accepted : 2012-01-01 Published : 2012-06-01

Keywords: eigenvalue, Generalized eigenvalue, Quadratic eigenvalue, Iterative method, Numerical computation,

Abstract :

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

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