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This article discusses a projection method for nonlinear eigenvalue problems. The subspace of approximants is constructed by a Jacobi–Davidson type approach, and the arising eigenproblems of small dimension are solved by safeguarded iteration. The method is applied to a rational eigenvalue problem governing the vibrations of tube bundle immersed in an(More)
We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on(More)
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary value problems. Its main drawback is that it often leads to ill-conditioned systems of equations. In this paper we investigate for the interior Helmholtz problem on analytic domains how the singularities (charge points) of the MFS basis functions have to be(More)
Conclusions High-accuracy solution of the Helmholtz BVP requires that coefficients α remain O(1), which in turn requires that the MFS charge curve enclose no singularities in the analytic continuation of the solution. We prove this, with convergence rates, in the disc. We devise a singularity-adapted charge curve for general analytic domains, and show this(More)
Coercivity is an important concept for proving existence and uniqueness of solutions to variational problems in Hilbert spaces. But, while the existence of coercivity estimates is well known for many variational problems arising from partial differential equations, it is still an open problem in the context of boundary integral operators arising from(More)
We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the L 2 condition numbers for these formulations, and also on the norms of the classical acoustic single-and double-layer potential operators. These(More)
Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems , for(More)