Observations on the behavior of radial basis function approximations near boundaries

[1]  R. L. Hardy.  Multiquadric equations of topography and other irregular surfaces , 1971 .

[2]  Jean Duchon,et al.  Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[3]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[4]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[5]  M. J. D. Powell.  Univariate Multiquadric Interpolation: Some Recent Results , 1991, Curves and Surfaces.

[6]  J. Hoschek,et al.  Scattered Data Interpolation , 1992 .

[7]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[8]  Bengt Fornberg,et al.  A practical guide to pseudospectral methods: Introduction , 1996 .

[9]  Radial Basis Functions Viewed From Cubic Splines , 1997 .

[10]  Benny Y. C. Hon,et al.  An efficient numerical scheme for Burgers' equation , 1998, Appl. Math. Comput..

[11]  Michelle Ghrist,et al.  Spatial Finite Difference Approximations for Wave-Type Equations , 1999, SIAM J. Numer. Anal..

[12]  Gregory E. Fasshauer,et al.  Solving differential equations with radial basis functions: multilevel methods and smoothing , 1999, Adv. Comput. Math..

[13]  E. Kansa,et al.  Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary , 2002 .

[14]  T. Driscoll,et al.  Interpolation in the limit of increasingly flat radial basis functions , 2002 .