Efficient Methods For Nonlinear Eigenvalue Problems Diploma Thesis
نویسنده
چکیده
During the last years nonlinear eigenvalue problems of the type T (λ)x = 0 became more and more important in many applications with the rapid development of computing performance. In parallel the minmax theory for symmetric nonlinear eigenvalue problems was developed which reveals a strong connection to corresponding linear problems. We want to review the current theory for symmetric nonlinear eigenvalue problems and give an overview about present solution methods for arbitrary nonlinear eigenvalue problems. Based on the theory for symmetric problems we will introduce a new solution method for large sparse symmetric nonlinear eigenvalue problems which combines a Jacobi-Davidson type approach with the theory for symmetric problems. With an example from fluid-structure interaction we demonstrate the high performance of the new algorithm and give ideas how to extend this approach for nonsymmetric problems.
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