On Curve Interpolation in Rd

Abstract

In this paper the interpolation by G(sup 2) continuous spline curves of degree n in IR(sup d) is studied. There are tau interior and two boundary data points interpolated on each segment of the spline curve. The general form of the spline curve, as well as the defining system of nonlinear equations are derived. The asymptotic existence of the solution, and the approximation order are studied for the polynomial case only. It is shown that the optimal approximation order is achieved, and asymptotic existence is established provided the relation tau = n - 2 is satisfied. These conclusions hold independently of d. It is also pointed out that the underlying analysis could not be carried over to the case tau = n - 1.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2000
Accession Number
ADP011994

Entities

People

  • Emil Zagar
  • Jernej Kozak

Organizations

  • University of Ljubljana

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Coefficients
  • Computer Programs
  • Computers
  • Continuity
  • Coordinate Systems
  • Curvature
  • Equations
  • Interpolation
  • Nonlinear Systems
  • Polynomials
  • Standards
  • Technical Information Centers

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Linear Algebra
  • Statistical inference.