AN ELASTIC FLOW FOR NONLINEAR SPLINE INTERPOLATIONS IN ℝn

Chun Chi Lin, Hartmut R. Schwetlick, Dung The Tran

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Abstract

In this paper we use the method of geometric flow on the problem of nonlinear spline interpolations for non-closed curves in n-dimensional Euclidean spaces. The method applies theory of fourth-order parabolic PDEs to each piece of the curve between two successive knot points at which certain dynamic boundary conditions are imposed. We show the existence of global solutions of the elastic flow in suitable Hölder spaces. In the asymptotic limit, as time approaches infinity, solutions subconverge to a stationary solution of the problem. The method of geometric flows provides a new approach for the problem of nonlinear spline interpolations.

Original languageEnglish
Pages (from-to)4893-4942
Number of pages50
JournalTransactions of the American Mathematical Society
Volume375
Issue number7
Early online date4 May 2022
DOIs
Publication statusPublished - 1 Jul 2022

Bibliographical note

This work was partially supported by the research grant of the National Science Council of Taiwan (NSC-100-2115-M-003-003), the National Center for Theoretical Sciences at Taipei, and the Max-Planck-Institut für Mathematik in den Naturwissenschaften in Leipzig. The third author received financial support from Taiwan MoST 108-2115-M-003-003-MY2.

Keywords

  • curve fitting
  • elastic spline
  • Fourth-order geometric flow
  • spline interpolation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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