Computation of eigenvalues of a real matrix

Authors:
S. Chandra Sekhara Rao
Affiliations:
Department of Mathematics, Indian Institute of Technology, New Delhi, India
Venue:
International Journal of Computer Mathematics
Year:
2008

Citing 3
Cited 0

The algebraic eigenvalue problem

The algebraic eigenvalue problem
Existence and uniqueness of WZ factorization

Parallel Computing
Parallel elimination method for general linear systems

Neural, Parallel & Scientific Computations

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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.