PhD research project

Project description

Two parameter eigenvalue problems are eigenvalue problems with two eigenvalue parameters instead of a single one as in the classical eigenvalue problem. Such eigenvalue problems arise, e.g., from the detection of the Hopf bifurcations of a dynamical system. For some applications, several eigenvalues of the two parameter eigenvalue problem need to be computed explicitly. A possible technique eliminates one of the parameters, resulting in a new single parameter eigenvalue problem named the Kronecker eigenvalue problem. The difficulty is that the size of the Kronecker eigenvalue problem is the square of the size of the original eigenvalue problem. This leads to computational challenges for keeping both memory usage and computational costs low. In this project, we aim at developing new and reliable solution techniques for the 'two parameter' eigenvalue problem. We distinguish between three main research items. First, we will analyse the algebraic structure of all involved matrices and exploit this in the development of efficient QR type methods for the small scale problem. Second, we will develop new Krylov style methods for large scale matrices. Third, we will investigate the connections with the higher order tensors and use these for developing alternative solution methods.

Researchers

• Nick Vannieuwenhoven
• Raf Vandebril (promotor)
• Karl Meerbergen (promotor)

Sponsored by