Abstract
In this talk, I consider solving parametric generalized eigenvalue problem using model order reduction techniques. My interest is on few of the eigenvalues that lie on the spectral interval of interest and the corresponding eigenvectors. All matrices are assumed to be s.p.d for any admissible parameter vector.
A Ritz method that uses the same subspace for any parameter value is developed. The Ritz subspace is designed using the observation that any eigenvector can be split to two components. The first component belongs to an easily computable subspace and the second component is associated to $(d+1)$ dimensional analytic function that can be approximated by sparse interpolation.
I give estimates for the approximation error and illustrate the method by numerical examples. The advantage of this approach is that the analysis easily treats eigenvalue crossings that typically have posed technical challenges in similar works.
Brief Biography
Antti Hannukainen was born in Pori, Finland, in 1981. He received the M.Sc. (Tech) degree from the Department of Electrical Engineering, Helsinki University of Technology, Espoo, Finland, and the D.Sc. (Tech) degree from the Department of Mathematics, Aalto University, Espoo, in 2007 and 2011, respectively. He was a researcher with RWTH Aachen, Aachen, Germany; a Visiting Researcher with the Vienna University of Technology, Vienna, Austria; and an Academy of Finland Post-Doctoral Researcher with the Department of Mathematics and Systems Analysis, Aalto University. Since 2014, he has been at the Department of Mathematics and System Analysis, Aalto University first as Assistant and currently as an Associate professor. His current research interests include model order reduction, parametric eigenvalue problems and solution of inverse problems.
