Design Problems for Optimal Surface Interpolation.

Abstract

We consider the problem of interpolating a surface given its values at a finite number of points. We place a special emphasis on the question of choosing the location of the points where the function will be sampled. Using minimal norm interpolation in reproducing kernel Hilbert spaces, equivalently Bayesian interpolation, and N-widths, we provide lower bounds for interpolation error relative to certain error criteria. These lower bounds can be used when evaluating an existing design, or when attempting to obtain a good design by iterative procedures to decide whether further minimization is worthwhile. The bounds are given in terms of the eigenvalues of a relevant reproducing kernel and the asymptotic behavior of these eigenvalues for certain tensor product spaces in the unit d-dimensional cube is obtained.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1979
Accession Number
ADA070012

Entities

People

  • Charles A. Micchelli
  • Grace Wahba

Organizations

  • University of Wisconsin Madison Department of Statistics

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Bayesian Networks
  • Convergence
  • Covariance
  • Data Science
  • Eigenvalues
  • Equations
  • Estimators
  • Experimental Design
  • Information Science
  • Integral Equations
  • Integrals
  • Mathematics
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • Surveys

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Space