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An approach based on dwindling filter method for positive definite generalized eigenvalue problem

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Abstract

In this paper, we present a new spectral residual method for solving large-scale positive definite generalized eigenvalue problems. The proposed algorithm is equipped with a dwindling multidimensional nonmonotone filter, in which the envelope dwindles as the step length decreases. We have also employed a relaxed nonmonotone line search technique in the structure of the algorithm which allows it to enjoy the nonmonotonicity from scratch. Under some mild and standard assumptions, the global convergence property of the proposed algorithm is established. An implementation of the new algorithm on some test problems shows the efficiency and effectiveness of the proposed algorithm in practice.

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Acknowledgements

The authors would like to thank the Research Council of K.N. Toosi University of Technology and the SCOPE Research Center for supporting this work.

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Authors and Affiliations

  1. Faculty of Mathematics, K.N. Toosi University of Technology, P.O.Box 16315-1618, Tehran, Iran

    F. Arzani & M. Reza Peyghami

  2. Scientific Computations in Optimization and Systems Engineering (SCOPE), K.N. Toosi University of Technology, Tehran, Iran

    F. Arzani & M. Reza Peyghami

Authors
  1. F. Arzani
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  2. M. Reza Peyghami
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Correspondence to M. Reza Peyghami.

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Communicated by Antonio José Silva Neto.

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Arzani, F., Peyghami, M.R. An approach based on dwindling filter method for positive definite generalized eigenvalue problem. Comp. Appl. Math. 37, 1197–1212 (2018). https://doi.org/10.1007/s40314-016-0391-z

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  • DOI: https://doi.org/10.1007/s40314-016-0391-z

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