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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 346, Pages 5–20 (Mi znsl83)  
Convergence analysis of an optimization algorithm for computing the largest eigenvalue of a symmetric matrix

A. N. Borzykh

Saint-Petersburg State University
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Abstract: A new optimization algorithm for computing the largest eigenvalue of a real symmetric matrix is considered. The algorithm is based on a sequence of plane rotations increasing the sum of the matrix entries. It is proved that the algorithm converges linearly and it is shown that it can be regarded as a relaxation method for the Rayleigh quotient.
Received: 01.10.2007
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 150, Issue 2, Pages 1917–1925
DOI: https://doi.org/10.1007/s10958-008-0105-1
Bibliographic databases:
UDC: 519.6
Language: Russian
Citation: A. N. Borzykh, “Convergence analysis of an optimization algorithm for computing the largest eigenvalue of a symmetric matrix”, Computational methods and algorithms. Part XX, Zap. Nauchn. Sem. POMI, 346, POMI, St. Petersburg, 2007, 5–20; J. Math. Sci. (N. Y.), 150:2 (2008), 1917–1925
Citation in format AMSBIB
\Bibitem{Bor07}
\by A.~N.~Borzykh
\paper Convergence analysis of an optimization algorithm for computing
the largest eigenvalue of a symmetric matrix
\inbook Computational methods and algorithms. Part~XX
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 346
\pages 5--20
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl83}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2469437}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 150
\issue 2
\pages 1917--1925
\crossref{https://doi.org/10.1007/s10958-008-0105-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-41149099084}
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