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

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.

Authors:
;  [1]
  1. K.N. Toosi University of Technology, Faculty of Mathematics (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22769354
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; EFFICIENCY; EIGENVALUES

Citation Formats

Arzani, F., E-mail: farzani@dena.kntu.ac.ir, and Peyghami, M. Reza, E-mail: peyghami@kntu.ac.ir. An approach based on dwindling filter method for positive definite generalized eigenvalue problem. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0391-Z.
Arzani, F., E-mail: farzani@dena.kntu.ac.ir, & Peyghami, M. Reza, E-mail: peyghami@kntu.ac.ir. An approach based on dwindling filter method for positive definite generalized eigenvalue problem. United States. doi:10.1007/S40314-016-0391-Z.
Arzani, F., E-mail: farzani@dena.kntu.ac.ir, and Peyghami, M. Reza, E-mail: peyghami@kntu.ac.ir. Tue . "An approach based on dwindling filter method for positive definite generalized eigenvalue problem". United States. doi:10.1007/S40314-016-0391-Z.
@article{osti_22769354,
title = {An approach based on dwindling filter method for positive definite generalized eigenvalue problem},
author = {Arzani, F., E-mail: farzani@dena.kntu.ac.ir and Peyghami, M. Reza, E-mail: peyghami@kntu.ac.ir},
abstractNote = {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.},
doi = {10.1007/S40314-016-0391-Z},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 2,
volume = 37,
place = {United States},
year = {2018},
month = {5}
}