Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods

The locally optimal block preconditioned 4-d conjugate gradient method （LOBP4dCG） for the linear response eigenvalue problem was proposed by Bai and Li （2013） and later was extended to the generalized linear response eigenvalue problem by Bai and Li （2014）. We put forward two improvements to the met...

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Bibliographic Details
Published inScience China. Mathematics Vol. 59; no. 8; pp. 1443 - 1460
Main Authors Bai, ZhaoJun, Li, RenCang, Lin, WenWei
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.08.2016
Subjects
Algorithms
Applications of Mathematics
Conjugate gradient method
Convergence
Eigenvalues
Mathematical models
Mathematics
Mathematics and Statistics
Optimization
Searching
Subspaces
共轭梯度方法
局部优化
局部最优
搜索子空间
收敛速度
特征值问题
线性响应
预条件共轭梯度法
linear response
81Q15
conjugate-gradient
65L15
deflation
eigenvalue problem
15A18
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ISSN1674-7283
1869-1862
DOI10.1007/s11425-016-0297-1

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Summary:The locally optimal block preconditioned 4-d conjugate gradient method （LOBP4dCG） for the linear response eigenvalue problem was proposed by Bai and Li （2013） and later was extended to the generalized linear response eigenvalue problem by Bai and Li （2014）. We put forward two improvements to the method： A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4dCG （ELOBP4dCG）. Numerical results of the ELOBP4dCG strongly demonstrate the capability of deflation technique and effec- tiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.
Bibliography:eigenvalue problem, linear response, deflation, conjugate-gradient, deflation
The locally optimal block preconditioned 4-d conjugate gradient method （LOBP4dCG） for the linear response eigenvalue problem was proposed by Bai and Li （2013） and later was extended to the generalized linear response eigenvalue problem by Bai and Li （2014）. We put forward two improvements to the method： A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4dCG （ELOBP4dCG）. Numerical results of the ELOBP4dCG strongly demonstrate the capability of deflation technique and effec- tiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-0297-1