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# 252-0504-00L  Numerical Methods for Solving Large Scale Eigenvalue Problems

 Semester Spring Semester 2015 Lecturers P. Arbenz Periodicity two-yearly recurring course Course Does not take place this semester. Language of instruction English

 Abstract In this lecture algorithms are investigated for solving eigenvalue problemswith large sparse matrices. Some of these eigensolvers have been developedonly in the last few years. They will be analyzed in theory and practice (by meansof MATLAB exercises). Objective Knowing the modern algorithms for solving large scale eigenvalue problems, their numerical behavior, their strengths and weaknesses. Content The lecture starts with providing examples for applications in whicheigenvalue problems play an important role. After an introductioninto the linear algebra of eigenvalue problems, an overview ofmethods (such as the classical QR algorithm) for solving small tomedium-sized eigenvalue problems is given.Afterwards, the most important algorithms for solving large scale,typically sparse matrix eigenvalue problems are introduced andanalyzed. The lecture will cover a choice of the following topics:* vector and subspace iteration* trace minimization algorithm* Arnoldi and Lanczos algorithms (including restarting variants)* Davidson and Jacobi-Davidson Algorithm* preconditioned inverse iteration and LOBPCG* methods for nonlinear eigenvalue problemsIn the exercises, these algorithm will be implemented (in simplified forms)and analysed in MATLAB. Lecture notes Lecture notes, Copies of slides Literature Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia, 2000.Y. Saad: Numerical Methods for Large Eigenvalue Problems. Manchester University Press, Manchester, 1994.G. H. Golub and Ch. van Loan: Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore 1996. Prerequisites / Notice Prerequisite: linear agebra