Abstract
In this paper I describe an algorithm for finding all of the eigenvalues and eigenvectors of an Hermitian matrix (either complex or real, symmetric). The algorithm is a combination of Householder reduction to tri-diagonal form and a modified QR method for obtaining both eigenvalues and eigenvectors of the reduced matrix. The central new practical technique communicated here lies in the modification of the QR method when generating eigenvectors along with the eigenvalues.
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References
J. H. Wilkinson, The Algebraic Eigenvalue Problem. Clarendon Press, Oxford (1965).
J. G. F. Francis, Computer J. 4, 265 and 332 (1961).
HECEVV is part of a larger package available from the GESHUA Library: HEMP — High Efficiency Matrix Package, GES1030, GE-600 Series Users’ Library. HEMP is written in assembly language for General Electric 600-Series computers.
W. Kahan and J. Varah, Computer Science Department Technical Report No. CS43, Stanford University (1966).
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© 1971 Plenum Press, New York
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Faulkner, R.A. (1971). Diagonalization of Hermitian Matrices; Maximization of Speed and Accuracy. In: Marcus, P.M., Janak, J.F., Williams, A.R. (eds) Computational Methods in Band Theory. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1890-3_2
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DOI: https://doi.org/10.1007/978-1-4684-1890-3_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-1892-7
Online ISBN: 978-1-4684-1890-3
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