Interpolation in the Limit of Increasingly Flat Radial Basis Functions

  title={Interpolation in the Limit of Increasingly Flat Radial Basis Functions},
  author={Tobin A. Driscoll and Bengt Fornberg},
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


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