Theorie, Störungsanalyse und numerische Verfahren für Produkteigenwertprobleme und deren Anwendungen

• Applicant: Professor Dr. Daniel Kressner
• Subject Area: Mathematics
• Term: from 2005 to 2008
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5449049

A variety of applications in chemistry, engineering and physics leads to structured eigenvalue problems, most of which can be viewed as particular instances of a product eigenvalue problem. This problem consists of computing the eigenvalues and invariant subspaces of a product of matrices. Working on its factors instead of the explicitly formed product has several important advantages, e.g., preservation of physically meaningful properties and higher accuracy in the computed eigenvalues. The aim of this project is to develop numerical algorithms that take this fact into account, guarantee high relative accuracy and allow the efficient solution of large-scale problems. To achieve this aim, several open issues regarding the theory and perturbation analysis for product eigenvalue problems have to be addressed. Based on these investigations, a high-quality software toolbox will be implemented comprising the ingredients of state-of-the-art numerical linear algebra software. This toolbox as well as the derived theoretical results will be used to address several applications, in particular those related to physical and chemical processes with seasonal or periodic behaviour. Other applications that will directly benefit from this work include optimal control problems, model reduction, bifurcation analysis and the computation of Floquet multipliers for partial differential equations.

• DFG Programme: Emmy Noether International Fellowships
• Hosts: Professor Dr. Zlatko Drmac; Professor Dr. Bo Kagström