论文信息 - On the least squares fit by radial functions to multidimensional scattered data

On the least squares fit by radial functions to multidimensional scattered data

SummaryThis paper investigates some aspects of discrete least squares approximation by translates of certain classes of radial functions. Its specific aims are (i) to provide conditions under which the associated least squares matrix is invertible and (ii) to give upper bounds for the Euclidean norms of the inverses of these matrices (when they exist).

J. Ward | N. Sivakumar

[1] I. J. Schoenberg. Metric spaces and completely monotone functions , 1938 .

[2] E. Cheney. Introduction to approximation theory , 1966 .

[3] Carl de Boor,et al. A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[4] Gene H. Golub,et al. Matrix computations , 1983 .

[5] C. Micchelli. Interpolation of scattered data: Distance matrices and conditionally positive definite functions , 1986 .

[6] D. Broomhead,et al. Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[7] Tomaso A. Poggio,et al. Extensions of a Theory of Networks for Approximation and Learning , 1990, NIPS.

[8] F. J. Narcowich,et al. Norms of inverses and condition numbers for matrices associated with scattered data , 1991 .

[9] K. Ball. Eigenvalues of Euclidean distance matrices , 1992 .

[10] F. J. Narcowich,et al. Norm estimates for the inverse of a general class of scattered-data radial-function interpolation matrices , 1992 .

[11] N. Sivakumar,et al. Least squares approximation by radial functions , 1993 .