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

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 emplo...

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Bibliographic Details
Published in:Computational & applied mathematics 2018-05, Vol.37 (2), p.1197-1212
Main Authors: Arzani, F., Peyghami, M. Reza
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Eigenvalues
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-016-0391-z