An Abstract Formulation of Variational Refinement

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, the theory of abstract splines is applied to the variational refinement of (periodic) curves that meet data to within convex sets in ℝd. The analysis is relevant to each level of refinement (the limit curves are not considered here). The curves are characterized by an application of a separation theorem for multiple convex sets, and represented as the solution of an equation involving the dual of certain maps on an inner product space. Namely, T* Tf + Λ̃* w Γ (Λ f) = 0. Existence and uniqueness are established under certain conditions. The problem here is a generalization of that studied in (Kersey, Near-interpolatory subdivided curves, author's home page, 2003) to include arbitrary quadratic minimizing functionals, placed in the setting of abstract spline theory. The theory is specialized to the discretized thin beam and interval tension problems.

Original languageAmerican English
JournalJournal of Approximation Theory
Volume130
DOIs
StatePublished - Oct 1 2004

Keywords

  • Abstract splines
  • Subdivision
  • Variational refinement

DC Disciplines

  • Education
  • Mathematics

Fingerprint

Dive into the research topics of 'An Abstract Formulation of Variational Refinement'. Together they form a unique fingerprint.

Cite this