Interpolation in the Limit of Increasingly Flat Radial Basis Functions

@inproceedings{Driscoll2002InterpolationIT,
  title={Interpolation in the Limit of Increasingly Flat Radial Basis Functions},
  author={Tobin A. Driscoll and Bengt Fornberg},
  year={2002}
}
Many types of radial basis functions, such as multiquadrics, contain a free parameter. In the limit where the basis functions become increasingly flat, the linear system to solve becomes highly ill-conditioned, and the expansion coefficients diverge. Nevertheless, we find in this study that limiting interpolants often exist and take the form of polynomials. In the 1-D case, we prove that with simple conditions on the basis function, the interpolants converge to the Lagrange interpolating… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 115 extracted citations

References

Publications referenced by this paper.
Showing 1-7 of 7 references

Observations on the behavior of radial basis functions near boundaries

  • B. Fornberg, T. A. Driscoll, G. Wright, R. Charles
  • Computers Math. Appl.,
  • 2001
1 Excerpt

The parameter R2 in multiquadric interpolation

  • R. E. Carlson, T. A. Foley
  • Computers Math. Appl., 21
  • 1991
3 Excerpts

The theory of radial basis function approximation in 1990

  • M.J.D. Powell
  • Advances in Numerical Analysis, Vol. II: Wavelets…
  • 1990
2 Excerpts

Nelson , Multivariate interpolation and conditionally positive definite functions

  • A. S.
  • II , Math . Camp .

Similar Papers

Loading similar papers…