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A new iterative method for simultaneous computation of several eigenpair derivatives of a large matrix

Author

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  • Xie, Huiqing
  • Lu, Manhong

Abstract

A new iterative method is proposed to simultaneously compute several eigenpair derivatives of a large matrix analytically dependent on parameters. By using the Krylov subspaces augmented with the eigenvectors that one wants to differentiate, computation of several eigenpair derivatives is reduced to solving several small linear least square problems at each iteration. Convergence properties of the proposed method are analyzed. A strategy is provided to accelerate the convergence of the proposed method. Finally the efficiency of the proposed method is illustrated with some numerical examples.

Suggested Citation

  • Xie, Huiqing & Lu, Manhong, 2024. "A new iterative method for simultaneous computation of several eigenpair derivatives of a large matrix," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    • Handle: RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324000985
    DOI: 10.1016/j.amc.2024.128626
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