Some observations regarding interpolants in the limit of flat radial basis functions

McLeod, 1998

Micchelli, 1986, Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Constr. Approx., 2, 11, 10.1007/BF01893414

Cheney, 2000

Powell, 1992, The theory of radial basis function approximation in 1990, 105

Wu, 1993, Local error estimates for radial basis function interpolation of scattered data, I.M.A. J. Numer. Anal., 13, 13

Madych, 1992, Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation, J. Approx. Theory, 70, 94, 10.1016/0021-9045(92)90058-V

Schaback, 1995, Error estimates and condition numbers for radial basis function interpolants, Adv. Comput. Math., 3, 251, 10.1007/BF02432002

Yoon, 2001, Spectral approximation orders of radial basis function interpolation on the Sobolev space, SIAM J. Math. Anal., 23, 946, 10.1137/S0036141000373811

Carlson, 1991, The parameter R2 in multiquadric interpolation, Computers Math. Applic., 21, 29, 10.1016/0898-1221(91)90123-L

Foley, 1994, Near optimal parameter selection for multiquadric interpolation, J. Appl. Sci. Comput., 1, 54

Rippa, 1999, An algorithm for selecting a good value for the parameter c in radial basis function interpolation, Adv. Comput. Math., 11, 193, 10.1023/A:1018975909870

Driscoll, 2002, Interpolation in the limit of increasingly flat radial basis functions, Computers Math. Applic., 43, 413, 10.1016/S0898-1221(01)00295-4

Fornberg, 1996

B. Fornberg and G. Wright, Stable computation of multiquadric interpolants for all values of the shape parameter, Computers Math. Applic. (to appear).

Larsson, 2003, A numerical study of some radial basis function based solution methods for elliptic PDEs, Computers Math. Applic., 46, 891, 10.1016/S0898-1221(03)90151-9

Powell, 2001, Radial basis function methods for interpolation to functions of many variables, University of Cambridge, DAMTP Report NA11

E. Larsson and B. Fornberg Theoretical aspects of multivariate interpolation with increasingly flat radial basis functions, Computers Math. Applic., (submitted).

B. Fornberg and N. Flyer, Accuracy of radial basis function derivative approximations in 1-D, Adv. Comput. Math., (submitted).

R. Schaback, Multivariate interpolation by polynomials and radial basis functions, (submitted).

Fornberg, 2002, Observations on the behavior of radial basis functions near boundaries, Computers Math. Applic., 43, 473, 10.1016/S0898-1221(01)00299-1