Masterproef T711 : Two-parameter eigenvalue problems

Begeleiding:

Informatie:	Marc Van Barel
Promotoren:	Marc Van Barel
Begeleider:	Marc Van Barel

Onderzoeksgroep:

Numerieke Approximatie en Lineaire Algebra Groep

Context:

Several problems in science and engineering can be formulated as a two-parameter eigenvalue problem: given square matrices A_i, B_i and C_i look for all vectors x and y and complex numbers λ and μ such that the following equations are satisfied:

A₁x = B₁λx + C₁μx

A₃y = B₂λy + C₂μy

Consider, e.g., a system of polynomial equations

p(λ,μ)=0

q(λ,μ)=0

in two variables λ and μ. This system can be linearized into a two-parameter eigenvalue problem.

Doel:

The aim of this thesis is to investigate existing methods and to design new methods to solve the two-parameter eigenvalue problem.

Uitwerking:

The research includes a study of the literature, the development of the theory and the corresponding numerical methods, the implementation and testing of these methods in Matlab, and applying those to nontrivial examples.

Relevante literatuur:

M. E. Hochstenbach, T. Kosir, B. Plestenjak: A Jacobi-Davidson type method for the two-parameter eigenvalue problem, SIAM J. Matrix Anal. Appl. 26 (2005) 477-497
B. Plestenjak, M. E. Hochstenbach: Roots of bivariate polynomial systems via determinantal representations, accepted in SIAM J. Sci. Comput., arXiv:1506.02291

Profiel:

Depending on the interest of the student, the focus can be more on theoretical aspects or more on developing and implementation of algorithms.

Deze masterproef is voor 1 of 2 studenten.