Summary
Givens's method of reducing a symmetric matrix to Jacobi form works equally well for skew symmetric matrices. The author shows how the eigenvalues of the resulting skew-symmetric Jacobi matrix are obtained with the aid of the Quotient Difference Algorithm [2]. The theory of continued fractions allows the QD-table for the negative squares of the eigenvalues to be set up direct, which considerably reduces computing time.
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Literaturverzeichnis
W. Givens,A Method of Computing Eigenvalues and Eigenvectors Suggested by Classical Results on Symmetric Matrices, Nat. Bur. Stand., Applied Math. Series,29, 117–122 (1953).
H. Rutishauser,Der Quotienten-Differenzen-Algorithmus, Mitteilung Nr. 7 aus dem Institut für angewandte Mathematik (Verlag Birkhäuser, Basel und Stuttgart 1957).
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Rutishauser, H. Zur Bestimmung der Eigenwerte schiefsymmetrischer Matrizen. Journal of Applied Mathematics and Physics (ZAMP) 9, 586–590 (1958). https://doi.org/10.1007/BF02424776
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DOI: https://doi.org/10.1007/BF02424776