An Arnoldi Method for Nonlinear Eigenvalue Problems
نویسندگان
چکیده
For the nonlinear eigenvalue problem T (λ)x = 0 we propose an iterative projection method for computing a few eigenvalues close to a given parameter. The current search space is expanded by a generalization of the shift-and-invert Arnoldi method. The resulting projected eigenproblems of small dimension are solved by inverse iteration. The method is applied to a rational eigenvalue problem governing damped vibrations of a structure. AMS subject classification: 65F15, 49G05.
منابع مشابه
A linear eigenvalue algorithm for the nonlinear eigenvalue problem
The Arnoldi method for standard eigenvalue problems possesses several attractive properties making it robust, reliable and efficient for many problems. Our first important result is a characterization of a general nonlinear eigenvalue problem (NEP) as a standard but infinite dimensional eigenvalue problem involving an integration operator denoted B. In this paper we present a new algorithm equi...
متن کاملProjection Methods for Nonlinear Sparse Eigenvalue Problems
This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.
متن کاملKrylov Methods for Nonlinear Eigenvalue Problems
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 ...
متن کاملNonlinear Rayleigh-ritz Iterative Method for Solving Large Scale Nonlinear Eigenvalue Problems
A nonlinear Rayleigh-Ritz iterative (NRRIT) method for solving nonlinear eigenvalue problems is studied in this paper. It is an extension of the nonlinear Arnoldi algorithm due to Heinrich Voss. The effienicy of the NRRIT method is demonstrated by comparing with inverse iteration methods to solve a highly nonlinear eigenvalue problem arising from finite element electromagnetic simulation in acc...
متن کاملIterative Projection Methods for Large–scale Nonlinear Eigenvalue Problems
In this presentation we review iterative projection methods for sparse nonlinear eigenvalue problems which have proven to be very efficient. Here the eigenvalue problem is projected to a subspace V of small dimension which yields approximate eigenpairs. If an error tolerance is not met then the search space V is expanded in an iterative way with the aim that some of the eigenvalues of the reduc...
متن کامل