Journal of Computational Physics
A Multilevel Jacobi-Davidson Method for Polynomial PDE Eigenvalue Problems Arising in Plasma Physics
SIAM Journal on Scientific Computing
NLEVP: A Collection of Nonlinear Eigenvalue Problems
ACM Transactions on Mathematical Software (TOMS)
An algorithm for the complete solution of quadratic eigenvalue problems
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.01 |
Scaling is a commonly used technique for standard eigenvalue problems to improve the sensitivity of the eigenvalues. In this paper we investigate scaling for generalized and polynomial eigenvalue problems (PEPs) of arbitrary degree. It is shown that an optimal diagonal scaling of a PEP with respect to an eigenvalue can be described by the ratio of its normwise and componentwise condition number. Furthermore, the effect of linearization on optimally scaled polynomials is investigated. We introduce a generalization of the diagonal scaling by Lemonnier and Van Dooren to PEPs that is especially effective if some information about the magnitude of the wanted eigenvalues is available and also discuss variable transformations of the type $\lambda=\alpha\mu$ for PEPs of arbitrary degree.