Abstract
In this paper, we present a new method, which is referred to as the Rayleigh quotient minimization method, for computing one extreme eigenpair of symmetric matrices. This method converges globally and attains cubic convergence rate locally. In addition, inexact implementations and its numerical stability of the Rayleigh quotient minimization method are explored. Finally, we use numerical experiments to demonstrate the convergence properties and show the competitiveness of the new method for solving symmetric eigenvalue problems.
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The authors are very much indebted to the referees for their constructive comments and valuable suggestions, which greatly improved the original manuscript of this paper.
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Communicated by Jinyun Yuan.
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Cun-Qiang Miao is supported by The National Natural Science Foundation of China (No. 11901361) and The Natural Science Foundation of Shandong Province (No. ZR2018BG002). Hao Liu is supported by The National Natural Science Foundation of China (No. 11401305 and No. 61573181).
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Miao, CQ., Liu, H. Rayleigh quotient minimization method for symmetric eigenvalue problems. Comp. Appl. Math. 38, 155 (2019). https://doi.org/10.1007/s40314-019-0962-x
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DOI: https://doi.org/10.1007/s40314-019-0962-x