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- Timo Betcke, Nicholas J. Higham, Volker Mehrmann, Christian Schröder, Françoise Tisseur
- ACM Trans. Math. Softw.
- 2013

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… (More)

- Alex H. Barnett, Timo Betcke
- J. Comput. Physics
- 2008

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.… (More)

- Timo Betcke, Lloyd N. Trefethen
- SIAM Review
- 2005

Fox, Henrici, and Moler made famous a “Method of Particular Solutions” for computing eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons. We explain why their formulation… (More)

- Lloyd N. Trefethen, Timo Betcke, MIMS EPrint
- 2005

Recently developed numerical methods make possible the highaccuracy computation of eigenmodes of the Laplacian for a variety of “drums” in two dimensions. A number of computed examples are presented… (More)

- Wojciech Smigaj, Timo Betcke, Simon R. Arridge, Joel Phillips, Martin Schweiger
- ACM Trans. Math. Softw.
- 2015

Many important partial differential equation problems in homogeneous media, such as those of acoustic or electromagnetic wave propagation, can be represented in the form of integral equations on the… (More)

- Timo Betcke, Euan A. Spence
- SIAM J. Numerical Analysis
- 2011

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… (More)

- Timo Betcke
- SIAM J. Scientific Computing
- 2008

A powerful method for solving planar eigenvalue problems is the Method of Particular Solutions (MPS), which is also well known under the name “point matching method”. The implementation of this… (More)

- Timo Betcke
- SIAM J. Matrix Analysis Applications
- 2008

Scaling is a commonly used technique for standard eigenvalue problems to improve the sensitivity of the eigenvalues. In this paper we investigate scaling for generalized and polynomial eigenvalue… (More)

- Alex H. Barnett, Timo Betcke
- SIAM J. Scientific Computing
- 2010

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions,… (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… (More)