Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem

Main Article Content

N. P. van der Aa
H. G. ter Morsche
R. R.M. Mattheij

Abstract

In many engineering applications, the physical quantities that have to be computed
are obtained by solving a related eigenvalue problem. The matrix under consideration and thus
its eigenvalues usually depend on some parameters. A natural question then is how sensitive the
physical quantity is with respect to (some of) these parameters, i.e., how it behaves for small changes
in the parameters. To find this sensitivity, eigenvalue and/or eigenvector derivatives with respect to
those parameters need to be found. A method is provided to compute first order derivatives of the
eigenvalues and eigenvectors for a general complex-valued, non-defective matrix.

Article Details

Section
Article