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Calculation of eigenpair derivatives for asymmetric damped systems with distinct and repeated eigenvalues
Author(s) -
Wang Pingxin,
Dai Hua
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4901
Subject(s) - eigenvalues and eigenvectors , invertible matrix , mathematics , computation , homogeneous , normalization (sociology) , quadratic equation , linear system , mathematical analysis , pure mathematics , algorithm , geometry , physics , combinatorics , quantum mechanics , sociology , anthropology
Summary An algorithm is derived for the computation of eigenpair derivatives of asymmetric quadratic eigenvalue problem with distinct and repeated eigenvalues. In the proposed method, the eigenvector derivatives of the damped systems are divided into a particular solution and a homogeneous solution. By introducing an additional normalization condition, we construct two extended systems of linear equations with nonsingular coefficient matrices to calculate the particular solution. The method is numerically stable, and the homogeneous solutions are computed by the second‐order derivatives of the eigenequations. Two numerical examples are used to illustrate the validity of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.