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A note on the Rayleigh quotient iteration for symmetric eigenvalue problems

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Abstract

The Rayleigh quotient iteration is a famous algorithm for solving symmetric eigenvalue problems but suffers a serious limitation: it does not converge in a few peculiar cases. In the present study we show that the Rayleigh quotient iteration always converges when the iterative vector is replaced. The main benefit of our proposed algorithm is that, unlike the existing modification that also guarantees convergence, it admits a direct convergence proof.

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Acknowledgments

The author would like to express his gratitude to Professor Takayasu Matsuo of the University of Tokyo for his comments and suggestions.

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Authors and Affiliations

  1. The University of Tokyo, Hongo7-3-1, Bunkyo-ku, Tokyo, Japan

    Kensuke Aishima

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  1. Kensuke Aishima
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Correspondence to Kensuke Aishima.

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The author is supported by JSPS Grant-in-Aid for Research Activity Start-up.

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Aishima, K. A note on the Rayleigh quotient iteration for symmetric eigenvalue problems. Japan J. Indust. Appl. Math. 31, 575–581 (2014). https://doi.org/10.1007/s13160-014-0148-2

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  • DOI: https://doi.org/10.1007/s13160-014-0148-2

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