Cubic Eigenvalue Problems

Aleksandra Kostić; Valentina Timotić; Amin Aganović

doi:10.5644/SJM.21.02.11

Authors

Aleksandra Kostić University of Sarajevo, Faculty of Mechanical Engineering, Vilsonovo šetalište 9, 71 000, Sarajevo, Bosnia and Herzegovina
Valentina Timotić University of East Sarajevo, Faculty of Philosophy, Alekse Šantića 1, 71420, Pale, Bosnia and Herzegovina
Amin Aganović University of Sarajevo, Faculty of Science, Zmaja od Bosne 33-35 , 71 000, Sarajevo, Bosnia and Herzegovina

DOI:

https://doi.org/10.5644/SJM.21.02.11

Keywords:

Cubic eigenvalue problem, algorithm for detecting hyperbolic cubic pencils, definite matrix pencils, variational characterization, linearization

Abstract

In this paper, we observe cubic eigenvalue problems, which belong to a special class of nonlinear eigenvalue problems. Degree of a cubic eigenvalue problem is relatively small, which allows us to determine some important properties of these problems. We present an algorithm to determine whether a cubic pencil is hyperbolic or not. Also, a definite cubic pencils will be considered. We use a variational characterization as a tool for solving cubic eigenvalue problems and compare the results with the application of the linearization method.

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