AN ELASTIC FLOW FOR NONLINEAR SPLINE INTERPOLATIONS IN ℝn

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

研究成果: 雜誌貢獻期刊論文同行評審

摘要

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.

原文英語
頁(從 - 到)4893-4942
頁數50
期刊Transactions of the American Mathematical Society
375
發行號7
DOIs
出版狀態已發佈 - 2022 7月 1

ASJC Scopus subject areas

  • 數學(全部)
  • 應用數學

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