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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hongxiu Zhong & Zhongming Teng & Guoliang Chen, 2019. "Weighted Block Golub-Kahan-Lanczos Algorithms for Linear Response Eigenvalue Problem," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:53-:d:195442
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