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Convergence analysis of an optimization algorithm for computing the largest eigenvalue of a symmetric matrix

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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 may be regarded as a relaxation method for the Rayleigh quotient. Bibliography: 6 titles.

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References

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    A. N. Borzykh

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  1. A. N. Borzykh
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Correspondence to A. N. Borzykh.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 5–20.

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Borzykh, A.N. Convergence analysis of an optimization algorithm for computing the largest eigenvalue of a symmetric matrix. J Math Sci 150, 1917–1925 (2008). https://doi.org/10.1007/s10958-008-0105-1

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  • DOI: https://doi.org/10.1007/s10958-008-0105-1

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