Abstract
We present an algorithm for approximating an eigensubspace of a spectral component of an analytic Fredholm valued function. Our approach is based on numerical contour integration and the analytic Fredholm theorem. The presented method can be seen as a variant of the FEAST algorithm for infinite dimensional nonlinear eigenvalue problems. Numerical experiments illustrate the performance of the algorithm for polynomial and rational eigenvalue problems.
Highlights
In this paper we study analytic operator eigenvalue problems defined on an open connected subset Ω ⊆ C in a separable Hilbert space H
Our approach is based on numerical contour integration and the analytic Fredholm theorem
The presented method can be seen as a variant of the FEAST algorithm for infinite dimensional nonlinear eigenvalue problems
Summary
In this paper we study analytic operator eigenvalue problems defined on an open connected subset Ω ⊆ C in a separable Hilbert space H. In this paper the numerical method is based on contour integrals of the generalized resolvent S−1. The state-of-the-art results in the contour integration based methods for solving nonlinear matrix eigenvalue problems are presented in [4,5,6] including the references therein. Results for contour integration based solution methods for Fredholm valued eigenvalue problems can be found in, for example, [7, 8]. Our algorithm consists of the inexact subspace iteration for the zeroth moment of the resolvent to construct the approximate eigenspace for the eigenvalues contained inside a contour Γ.
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