NONLINEAR RAYLEIGH-RITZ ITERATIVE METHOD FOR SOLVING LARGE SCALE NONLINEAR EIGENVALUE PROBLEMS

Nonlinear 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...

Iterative 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...

Solving nonlinear eigenvalue problems

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least k column vectors, where k is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show t...

On Rayleigh-Ritz Method in Three-Parameter Eigenvalue Problems

This paper deals with the computation of the eigenvalues of a three-parameter Sturm-Liouville problem in the form of ordinary differential equation using Rayleigh-Ritz Method, a method which is based on the principle of variational methods. This method has been effective in computing the eigenvalues of self-adjoint problems. The resulting equations obtained in applying Rayleigh-Ritz method on t...