Approximation Theory and Its Applications

, Volume 17, Issue 4, pp 36–57 | Cite as

Hilbertian Approach for Univariate Spline with Tension

  • A. Bouhamidi
Article

Abstract

In this work, a new approach is proposed for constructing splines with tension. The basic idea is in the use of distributions theory, which allows us to define suitable Hilbert spaces in which the tension spline minimizes some energy functional. Classical orthogonal conditions and characterizations of the spline in terms of a fundamental solution of a differential operator are provided. An explicit representation of the tension spline is given. The tension spline can be computed by solving a linear system. Some numerical examples are given to illustrate this approach.

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A. Bouhamidi
    • 1
  1. 1.Université du LittoralFrance

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