• 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 ofExpand
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Multiresolution analysis, Haar bases, and self-similar tilings of Rn
TLDR
Orthonormal bases for L/sup 2/(R/sup n/) are constructed that have properties that are similar to those enjoyed by the classical Haar basis. Expand
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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 andExpand
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Miscellaneous error bounds for multiquadric and related interpolators
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, forExpand
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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 aExpand
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An estimate for multivariate interpolation II
  • W. Madych
  • Computer Science, Mathematics
  • J. Approx. Theory
  • 1 October 2006
TLDR
We obtain an estimate of the LP(Ω) norm of u in terms of the lp norm of these values and the Lp norms of its mth order derivatives. Expand
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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 continuityExpand
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Cardinal Interpolation with Gaussian Kernels
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 LpExpand
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Tomography, Approximate Reconstruction, and Continuous Wavelet Transforms
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 ofExpand
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Interpolation of functions from generalized Paley-Wiener spaces
TLDR
We consider the problem of reconstruction of functions f from generalized Paley-Wiener spaces in terms of their values on complete interpolating sequence {Zn} and exhibit an explicit solution to the problem. Expand
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