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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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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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