Řešení symetrického problému vlastních čísel se zaměřením na dynamiku železničních kol

Abstract

This thesis contains an introduction to the eigenvalue problem. It discusses the possibilities of its use and shows some methods on how this problem can be solved. There are three examples where the eigenvalues are applied to real situations, which show that this is not just a theoretical problem and attention must be paid to it. The work deals with the performance of several methods for calculating eigenvalues, some of which implemented in Matlab and then tested. The results are analyzed and based on them, the previous implementation is being improved. At the end of the work, an outline of a new branch of methods is given,with preconditioned eigensolvers, which will be the subject of further research.