Krylov Methods for Nonlinear Eigenvalue Problems
نویسندگان
چکیده
We present two generalisations of the Krylov subspace method, Arnoldi for the purpose of applying them to nite dimensional eigenvalue problems nonlinear in the eigenvalue parameter. The rst method is called nonlinear rational Krylov subspace and approximates and updates the projection of a linearised problem by nesting a one-sided secant method with Arnoldi. The second method, called nonlinear Arnoldi, iteratively solves a sequence of projected nonlinear problems and has a convergence behaviour similar to residual inverse iteration. Both algorithms are successfully applied to one problem from modelling of uid-structure interaction and another from vibration analysis of objects with non-proportional damping. Numerical experiments with the two algorithms indicate large di erences mostly in favour of nonlinear Arnoldi, in both speed of convergence and robustness. Krylovmetoder för ickelinjära egenvärdesproblem
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