Computation of eigenvalues of a real matrix

Abstract

This paper presents a computational procedure for finding eigenvalues of a real matrix based on Alternate Quadrant Interlocking Factorization, a parallel direct method developed by Rao in 1994 for the solution of the general linear system Ax=b. The computational procedure is similar to LR algorithm as studied by Rutishauser in 1958 for finding eigenvalues of a general matrix. After a series of transformations the eigenvalues are obtained from simple 2×2 matrices derived from the main and cross diagonals of the limit matrix. A sufficient condition for the convergence of the computational procedure is proved. Numerical examples are given to demonstrate the method.

Keywords:

• alternate quadrant interlocking factorization
• eigenvalues and eigenvectors

2000 AMS Subject Classification :

• 65F15

CCS Category :

• G.1.3

Acknowledgements

The author gratefully acknowledges the valuable comments and suggestions from the anonymous referees.