Nonlinear Eigenvalue Problems with Specified Eigenvalues

Nonlinear Eigenvalue Problems with Specified Eigenvalues

This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T , we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed algebraic multiplicities. While the usual resolvent norm addresses this question for a single eigenvalue of multiplicity one, the general sett...

Generalized Eigenvalue Problems with Specified Eigenvalues

We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications. First, the characterization yields a singular value formula for determining the nearest pencil whose eigenvalues lie in a...

Nonlinear Eigenvalue Problems

Heinrich Voss Hamburg University of Technology 115.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-2 115.2 Analytic matrix functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115-3 115.3 Variational Characterization of Eigenvalues . . . . . . . . 115-7 115.4 General Rayleigh Functionals . . . . . . . . . . . . . . . . . . . ...

Solving nonlinear eigenvalue problems

Matrix polynomials with specified eigenvalues

Article history: Received 25 January 2014 Accepted 9 October 2014 Available online 5 November 2014 Submitted by F. Dopico MSC: 65F15 65F18 47A56