Weighted Block Golub-Kahan-Lanczos Algorithms for Linear Response Eigenvalue Problem

Hongxiu Zhong, Zhongming Teng and Guoliang Chen
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Hongxiu Zhong: School of Science, Jiangnan University, Wuxi 214122, China
Zhongming Teng: College of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou 350002, China
Guoliang Chen: School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China

Mathematics, 2019, vol. 7, issue 1, 1-15

Abstract: In order to solve all or some eigenvalues lied in a cluster, we propose a weighted block Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem. Error bounds of the approximations to an eigenvalue cluster, as well as their corresponding eigenspace, are established and show the advantages. A practical thick-restart strategy is applied to the block algorithm to eliminate the increasing computational and memory costs, and the numerical instability. Numerical examples illustrate the effectiveness of our new algorithms.

Keywords: linear response eigenvalue problem; block methods; weighted Golub-Kahan-Lanczos algorithm; convergence analysis; thick restart (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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