Smoothest Local Interpolation Formulas for Equally Spaced Data.

Abstract

Let a moving-average interpolation formula for equally spaced data, exact for the degree r, have a basic function L e C to the m-1 power of finite support with L to the (m) power piecewise continuous. Such a formula is called 'smoothest' when the integral of the square of L to the (m) power over the support of L is smallest. If m, r, and the support of L are given, either there is no such formula or there is a unique smoothest formula, for which L is a piecewise polynomial of degree at least r and at most max(r, 2m - 1), uniquely characterized by certain conditions on the location of its knots and the jumps occurring there. A similar result is obtained if consideration is limited to formulas that preserve (i.e., do not smooth) the given data.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1981
Accession Number
ADA103860

Entities

People

  • Hubert Vaughan
  • Thomas N.E. Greville

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Discontinuities
  • Equations
  • Extrapolation
  • Inequalities
  • Integrals
  • Interpolation
  • Intervals
  • Linear Systems
  • Mathematics
  • Numbers
  • Polynomials
  • Precision
  • Probability
  • Probability Distributions
  • United States

Fields of Study

  • Mathematics

Readers

  • Aerospace Engineering
  • Calculus or Mathematical Analysis
  • Statistical inference.

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  • Space
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