论文信息 - Lebesgue function for multivariate interpolation by radial basis functions

Lebesgue function for multivariate interpolation by radial basis functions

Multivariate interpolation and approximation is a powerful tool for intuition of real world. In this paper we study Lebesgue function and Lebesgue constant for multivariate interpolation by conditionally positive definite RBFs. Also we give a conjecture about similar Bernstein and Erdos problem to multivariate case.

Bahman Mehri | Sadegh Jokar

[1] Ward Cheney,et al. A course in approximation theory , 1999 .

[2] Theodore Kilgore. A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm , 1978 .

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

[4] A. Iske. On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines , 2003 .

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

[6] Paul Erdös,et al. Problems and results on the theory of interpolation. II , 1958 .

[7] E. Wagner. International Series of Numerical Mathematics , 1963 .

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

[9] Allan Pinkus,et al. Proof of the conjectures of Bernstein and Erdös concerning the optimal nodes for polynomial interpolation , 1978 .