Scattered Data Near-Interpolation with Application to Discontinuous Surfaces

Abstract

This paper discusses a particular type of function approximation on scattered data in a general number of variables, and its application to surface representation with imposed conditions. If the given function values are subject to errors, it is not appropriate to interpolate the function at the data in the sense of exact matching. As a consequence, we formulate a weakened version of the classical scattered data interpolation problem, and give a simple and efficient procedure to obtain near-interpolation formulas. Near-interpolants enjoy many remarkable properties, which are very useful from both theoretical and practical points of view (shape preserving properties, operator positivity, subdivision techniques, parallel and multistage computation). Applications of near-interpolants to the representation of surfaces, in particular with faults, are discussed in detail (parameter values, localizing weights, etc.).

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP011975

Entities

People

  • Giampietro Allasia
  • Renata Besenghi

Organizations

  • University of Turin

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Computations
  • Data Sets
  • Differential Equations
  • Discontinuities
  • Engineering
  • Equations
  • Errors
  • Geodesy
  • Interpolation
  • Least Squares Method
  • Models
  • Parallel Computing
  • Partial Differential Equations
  • Physics
  • Technical Information Centers

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.