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During the last decade, three main variations have been proposed for solving elliptic PDEs by means of collocation with radial basis functions (RBFs). In this study, we have implemented them for infinitely smooth RBFs, and then compared them across the full range of values for the shape parameter of the RBFs. This was made possible by a recently discovered… (More)

- Bengt Fornberg, Elisabeth Larsson, Natasha Flyer
- SIAM J. Scientific Computing
- 2011

Radial basis function (RBF) approximation is an extremely powerful tool for representing smooth functions in non-trivial geometries, since the method is meshfree and can be spectrally accurate. A perceived practical obstacle is that the interpolation matrix becomes increasingly illconditioned as the RBF shape parameter becomes small, corresponding to flat… (More)

- Elisabeth Larsson
- SIAM J. Scientific Computing
- 1999

- Bengt Fornberg, Elisabeth Larsson, Grady B. Wright
- Computers & Mathematics with Applications
- 2006

Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only non-oscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as their limiting case)… (More)

In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black–Scholes partial differential equation. As an example of a financial contract that can be priced with this method we have chosen the multi-dimensional European basket call option. We have shown numerically that our scheme is… (More)

- Kurt Otto, Elisabeth Larsson
- SIAM J. Matrix Analysis Applications
- 1999

The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The speciic problem is the propagation of hydroacoustic waves in a two-dimensional curvilinear duct. The problem is discretized with a second-order accurate nite-diierence method, resulting in a linear system of equations. To solve the system of… (More)

We show that the generalized Fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multidimensional option pricing. We derive a general algorithm, including a transformation of the Black–Scholes equation into the heat equation, that can be used in any number of dimensions. Numerical… (More)

Multivariate interpolation of smooth data using smooth radial basis functions is considered. The behavior of the interpolants in the limit of nearly flat radial basis functions is studied both theoretically and numerically. Explicit criteria for different types of limits are given. Using the results for the limits, the dependence of the error on the shape… (More)

- Elisabeth Larsson, Erik Lehto, Alfa R. H. Heryudono, Bengt Fornberg
- SIAM J. Scientific Computing
- 2013

Abstract. Radial basis function (RBF) approximation has the potential to provide spectrally accurate function approximations for data given at scattered node locations. For smooth solutions, the best accuracy for a given number of node points is typically achieved when the basis functions are scaled to be nearly flat. This also results in nearly linearly… (More)

- Martin Tillenius, Elisabeth Larsson, Rosa M. Badia, Xavier Martorell
- ACM Trans. Embedded Comput. Syst.
- 2015

Dependency-aware task-based parallel programming models have proven to be successful for developing efficient application software for multicore-based computer architectures. The programming model is amenable to programmers, thereby supporting productivity, whereas hardware performance is achieved through a runtime system that dynamically schedules tasks… (More)