Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions

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

[2]  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 .

[3]  E. Kansa Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[4]  R. L. Hardy Theory and applications of the multiquadric-biharmonic method : 20 years of discovery 1968-1988 , 1990 .

[5]  R. E. Carlson,et al.  The parameter R2 in multiquadric interpolation , 1991 .

[6]  Zongmin Wu,et al.  Hermite-Birkhoff interpolation of scattered data by radial basis functions , 1992, Approximation Theory and its Applications.

[7]  W. Madych,et al.  Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation , 1992 .

[8]  W. R. Madych,et al.  Miscellaneous error bounds for multiquadric and related interpolators , 1992 .

[9]  Nira Dyn,et al.  Spectral convergence of multiquadric interpolation , 1993, Proceedings of the Edinburgh Mathematical Society.

[10]  Zongmin Wu,et al.  Local error estimates for radial basis function interpolation of scattered data , 1993 .

[11]  Interpolation of curves and surfaces , 1994 .

[12]  M. Golberg,et al.  Improved multiquadric approximation for partial differential equations , 1996 .

[13]  Robin J. Y McLeod,et al.  Geometry and Interpolation of Curves and Surfaces , 1998 .

[14]  Carsten Franke,et al.  Solving partial differential equations by collocation using radial basis functions , 1998, Appl. Math. Comput..

[15]  A. Bejancu Local Accuracy for Radial Basis Function Interpolation on Finite Uniform Grids , 1999 .

[16]  F. J. Narcowich,et al.  Multilevel Interpolation and Approximation , 1999 .

[17]  Shmuel Rippa,et al.  An algorithm for selecting a good value for the parameter c in radial basis function interpolation , 1999, Adv. Comput. Math..

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

[19]  Robert Schaback,et al.  Improved error bounds for scattered data interpolation by radial basis functions , 1999, Math. Comput..

[20]  E. Kansa,et al.  Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations , 2000 .

[21]  Richard K. Beatson,et al.  Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods , 2000, SIAM J. Sci. Comput..

[22]  Richard K. Beatson,et al.  Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in Rn , 2001, SIAM J. Sci. Comput..

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

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

[25]  B. Fornberg,et al.  A numerical study of some radial basis function based solution methods for elliptic PDEs , 2003 .

[26]  B. Fornberg,et al.  Some observations regarding interpolants in the limit of flat radial basis functions , 2003 .

[27]  E. Kansa,et al.  Exponential convergence and H‐c multiquadric collocation method for partial differential equations , 2003 .

[28]  A. U.S.,et al.  Stable Computation of Multiquadric Interpolants for All Values of the Shape Parameter , 2003 .

[29]  R. Schaback Multivariate Interpolation by Polynomials and Radial Basis Functions , 2005 .