A simple algorithm for the computation of eigenvalues of real or complex square matrices is proposed. This algorithm is based on an additive decomposition of the matrix. A sufficient condition for convergence is proved. It is also shown that this method has many properties of the QR algorithm : it is invariant for the Hessenberg form, shifts axe possible in the case of a null element on the diagonal. Some other interesting experimental properties are shown. Numerical experiments are given showing that most of the time the behavior of this method is not much different from that of the QR method, but sometimes it gives better results, particularly in the case of a bad conditioned real matrix having real eigenvalues. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Alt, R. (2007). A simple and efficient algorithm for eigenvalues computation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4310 LNCS, pp. 271–278). Springer Verlag. https://doi.org/10.1007/978-3-540-70942-8_32
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