Reconstruction of Structured Quadratic Pencils from Eigenvalues on Ellipses and Parabolas

Authors

R. Ibragimov
Vesselin Vatchev, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

7-17-2014

Abstract

In the present paper we study the reconstruction of a structured quadratic pencil from eigenvalues distributed on ellipses or parabolas. A quadratic pencil is a square matrix polynomial

QP(λ) = M λ²+Cλ +K,

where M, C, and K are real square matrices. The approach developed in the paper is based on the theory of orthogonal polynomials on the real line. The results can be applied to more general distribution of eigenvalues. The problem with added single eigenvector is also briefly discussed. As an illustration of the reconstruction method, the eigenvalue problem on linearized stability of certain class of stationary exact solution of the Navier-Stokes equations describing atmospheric flows on a spherical surface is reformulated as a simple mass-spring system by means of this method.

Comments

© 2014, EDP Sciences. Original published version available at https://doi.org/10.1051/mmnp/20149509.

Recommended Citation

Ibragimov, R., and V. Vatchev. 2014. “Reconstruction of Structured Quadratic Pencils from Eigenvalues on Ellipses and Parabolas.” Mathematical Modelling of Natural Phenomena 9 (5): 138–47. https://doi.org/10.1051/mmnp/20149509.

First Page

138

Last Page

147

Publication Title

Mathematical Modelling of Natural Phenomena

DOI

10.1051/mmnp/20149509