On the Permanence Property in Spherical Spline Interpolation,

Abstract

Spherical spline functions are introduced by use of Green's (surface) functions with respect to the Beltrami operator on the sphere. The method of interpolation by spherical splines is formulated as variational problem of minimizing a (Sobolev) 'energy' norm under interpolatory constraints. The process is constructed so as to have the so - called performance property, i.e. the transition from the interpolating spline with respect to N data to the interpolating spline with respect to N + 1 data necessitates merely the addition of one more term, all the terms obtained formerly remaining unchanged. The algorithm is numerically stable and very economical as regards the number of operations.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1982
Accession Number
ADA126263

Entities

People

  • Willi Freeden

Organizations

  • Ohio State University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Applied Mathematics
  • Cartesian Coordinates
  • Computations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Geodesy
  • Hilbert Space
  • Identities
  • Integral Equations
  • Linear Systems
  • New York
  • Spherical Harmonics
  • Theorems
  • Three Dimensional

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)