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Derivatives of eigenvalues and eigenvectors of a general complex matrix
Author(s) -
Murthy Durbha V.,
Haftka Raphael T.
Publication year - 1988
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.1620260202
Subject(s) - eigenvalues and eigenvectors , hermitian matrix , mathematics , algebraic number , matrix (chemical analysis) , defective matrix , eigenvalue perturbation , sensitivity (control systems) , algebra over a field , pure mathematics , symmetric matrix , mathematical analysis , diagonalizable matrix , physics , engineering , materials science , quantum mechanics , electronic engineering , composite material
A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non‐Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.