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Bestimmung der Eigenwerte und Eigenvektoren einer Matrix mit Hilfe des Quotienten-Differenzen-Algorithmus

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Summary

Two previous papers (in Vol. V) describe theory and some applications of the quotient-difference (=QD-) algorithm. Here we give an extension which allows the determination of the eigenvectors of a matrix. Letx 1(0) , ...,x n(0) be a coordinate system in whichA has Jacobi form (such a system may be constructed with methods ofC. Lanczos orW. Givens). Then the QD-algorithm allows the construction of a sequence of coordinate systemsx 1(2μ) , ...,x n(2μ) , (μ=0, 1, 2, ...) which converge for μ≠∞ to the system of the eigenvectors ofA.

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Literaturverzeichnis

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  1. Institut für angewandte Mathematik der ETH, Zürich, Switzerland

    Heinz Rutishauser

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  1. Heinz Rutishauser
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Rutishauser, H. Bestimmung der Eigenwerte und Eigenvektoren einer Matrix mit Hilfe des Quotienten-Differenzen-Algorithmus. Journal of Applied Mathematics and Physics (ZAMP) 6, 387–401 (1955). https://doi.org/10.1007/BF01589764

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  • DOI: https://doi.org/10.1007/BF01589764

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