The proposed project aims at developing, analyzing, and implementing methods for a number of structured eigenvalue problems, and exploiting the results in applications. Specifically, the goals of this research are (1) further development and analysis of the Jacobi-Davidson type method for the singular value problem, and development of other two-sided subspace methods for this problem; (2) application of the methods to for instance least squares problems; (3) study of novel techniques for the polynomial eigenvalue problem and the J-symmetric (in particular Hamiltonian) eigenvalue problem; and (4) implementation of the methods in state-of-the-art Matlab and/or C code. The emphasis will be on the development and usage of promising and powerful techniques, exploiting the structure of the particular eigenvalue problems. These techniques include two-sided subspace approaches, Jacobi-Davidson type subspace expansion and harmonic and refined subspace extraction.
Eigenvalue problems arise in science, engineering, and daily life. The methods that will be developed have numerous applications in areas such as: - information retrieval and data mining (internet search engines), - image processing and medical imaging (removal of noise and blur from an image), - face recognition, - statistics, and mechanics (design of earthquake resistant buildings or wind resistant bridges).
