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Calculation of eigenpair derivatives for symmetric quadratic eigenvalue problem with repeated eigenvalues

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Abstract

In this paper, we consider computing the derivatives of the semisimple eigenvalues and corresponding eigenvectors of symmetric quadratic eigenvalue problem. In the proposed method, the eigenvector derivatives of the symmetric quadratic eigenvalue problem are divided into a particular solution and a homogeneous solution; a simplified method is given to calculate the particular solution by solving a linear system with nonsingular coefficient matrix, the method is numerically stable and efficient. Two numerical examples are included to illustrate the validity of the proposed method.

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Acknowledgments

The authors would like to express their heartfelt thanks to Professor Jinyun Yuan (Associate Editor) and an anonymous referee for their useful comments and suggestions which helped to improve the presentation of this paper.

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Authors and Affiliations

  1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Pingxin Wang & Hua Dai

  2. School of Mathematics and Physics, Jiangsu University of Science and Technology, Nanjing, 212003, Zhengjiang, People’s Republic of China

    Pingxin Wang

Authors
  1. Pingxin Wang
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  2. Hua Dai
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Corresponding author

Correspondence to Hua Dai.

Additional information

Communicated by Jinyun Yuan.

This work was supported by Defense Basic Research Program of China (No. J152013xxx) and National Natural Science Foundation of China (No. 11071118).

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Wang, P., Dai, H. Calculation of eigenpair derivatives for symmetric quadratic eigenvalue problem with repeated eigenvalues. Comp. Appl. Math. 35, 17–28 (2016). https://doi.org/10.1007/s40314-014-0169-0

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  • DOI: https://doi.org/10.1007/s40314-014-0169-0

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