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Publications Influence

Multivariate interpolation and condi-tionally positive definite functions

We continue an earlier study of certain spaces that provide a variational framework for multivariate interpolation. Using the Fourier transform to analyze these spaces, we obtain error estimates of… Expand

531 27- PDF

Multiresolution analysis, Haar bases, and self-similar tilings of Rn

- K. Gröchenig, W. Madych
- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1 March 1992

TLDR

349 22- PDF

Polyharmonic cardinal splines

Abstract Polyharmonic splines, sometimes called thin plate splines, are distributions which are annihilated by iterates of the Laplacian in the complement of a discrete set in Euclidean n -space and… Expand

121 15

Miscellaneous error bounds for multiquadric and related interpolators

- W. Madych
- Mathematics
- 1 December 1992

We establish several types of a a priori error bounds for multiquadric and related interpolators. The results are stated and proven in the general multivariate case. These estimates show, for… Expand

218 13

Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation

A class of multivariate scattered data interpolation methods which includes the so-called multiquadrics is considered. Pointwise error bounds are given in terms of several parameters including a… Expand

224 11

An estimate for multivariate interpolation II

- W. Madych
- Computer Science, Mathematics
- J. Approx. Theory
- 1 October 2006

TLDR

45 3

Polyharmonic cardinal splines: a minimization property

Abstract Polyharmonic cardinal splines are distributions which are annihilated by iterates of the Laplacian in the complement of a lattice in Euclidean n -space and satisfy certain continuity… Expand

36 3

Cardinal Interpolation with Gaussian Kernels

- T. Hangelbroek, W. Madych, F. J. Narcowich, J. Ward
- Mathematics
- 18 August 2010

In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes Lp Sobolev error estimates and shows that the error is controlled by the Lp… Expand

18 3- PDF

Tomography, Approximate Reconstruction, and Continuous Wavelet Transforms

- W. Madych
- Mathematics
- 1 July 1999

Abstract It has been recognized for some time now that certain high-frequency information concerning planar densities f in a neighborhood of a point can be recovered from data which consist of… Expand

23 2- PDF

Interpolation of functions from generalized Paley-Wiener spaces

- Y. Lyubarskii, W. Madych
- Computer Science, Mathematics
- J. Approx. Theory
- 1 April 2005

TLDR

8 2