Corpus ID: 145051633

Convergence of stationary radial basis function-schemes for evolution equations

  title={Convergence of stationary radial basis function-schemes for evolution equations},
  author={Bradley John Charles Baxter and Raymond Brummelhuis},
  journal={arXiv: Numerical Analysis},
We establish precise convergence rates for semi-discrete schemes based on Radial Basis Function interpolation, as well as approximate approximation results for such schemes. Our schemes use stationary interpolation on regular grids, with basis functions from a general class of functions generalizing one introduced earlier by M. Buhmann. Our results apply to parabolic equations such as the heat equation or Kolmogorov-Fokker-Planck equations associated to L\'evy processes, but also to certain… Expand


A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models
Abstract We use Radial Basis Function (RBF) interpolation to price options in exponential Lévy models by numerically solving the fundamental pricing PIDE (Partial integro-differential equations). OurExpand
On approximate approximations using Gaussian kernels
This paper discusses quasi-interpolation and interpolation with Gaussians. Estimates are obtained showing a high-order approximation up to some saturation error negligible in numerical applications.Expand
Scattered Data Approximation
1. Applications and motivations 2. Hear spaces and multivariate polynomials 3. Local polynomial reproduction 4. Moving least squares 5. Auxiliary tools from analysis and measure theory 6. PositiveExpand
Improved radial basis function methods for multi-dimensional option pricing
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 aExpand
Multivariate cardinal interpolation with radial-basis functions
AbstractFor a radial-basis functionϕ∶ℛ→ℛ we consider interpolation on an infinite regular lattice, tof∶ℛn→ℛ, whereh is the spacing between lattice points and the cardinal function, satisfiesX(j)=δojExpand
A parallel time stepping approach using meshfree approximations for pricing options with non-smooth payoffs
In this paper we consider a meshfree radial basis function approach for the valuation of pricing options with non-smooth payoffs. By taking advantage of parallel architecture, a strongly stable andExpand
Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation
A class of multivariate scattered data interpolation methods which includes the so-called multiquadrics is considered. Pointwise error bounds are given in terms of several parameters including aExpand
Meshfree Approximation Methods with Matlab
  • G. Fasshauer
  • Mathematics, Computer Science
  • Interdisciplinary Mathematical Sciences
  • 2007
This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods with the emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Expand
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
PrefaceGuide to the ReaderPrologue3IReal-Variable Theory7IIMore About Maximal Functions49IIIHardy Spaces87IVH[superscript 1] and BMO139VWeighted Inequalities193VIPseudo-Differential and SingularExpand