On Calculating with Lower Order Chebyshev Splines

Abstract

We develop a technique to calculate with Chebyshev Splines of orders 3 and 4, based on the known derivative formula for Chebyshev splines and an Oslo type algorithm. We assume that splines in the reduced system are simple enough to calculate. Local bases of Chebyshev splines of order 3 and 4 can thus be evaluated as positive linear combinations of less smooth Chebyshev B-splines. The coefficients in such linear combinations are discrete Chebyshev splines, normalized so as to make a partition of unity. There are a number of interesting special cases, such as Foley's upsilon-splines, Chebyshev polynomial splines (q-splines), and splines in tension which can be calculated stably by such formula.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP012045

Entities

People

  • Mladen Rogina
  • Tina Bosner

Organizations

  • University of Zagreb

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Chebyshev Polynomials
  • Coefficients
  • Construction
  • Elastic Properties
  • Equations
  • Euler Equations
  • Intervals
  • Linear Systems
  • Materials
  • Modulus Of Elasticity
  • Moment Of Inertia
  • Polynomials
  • Standards
  • Technical Information Centers

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Atmospheric Science/Meteorology
  • Mathematical Modeling and Probability Theory.