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Article
Mixed Interpolating-Smoothing Splines and the V-Spline
Journal of Mathematical Analysis and Applications
  • Scott N. Kersey, Georgia Southern University
Document Type
Article
Publication Date
10-1-2006
DOI
10.1016/j.jmaa.2005.07.007
Disciplines
Abstract

In their monograph, Bezhaev and Vasilenko have characterized the “mixed interpolating–smoothing spline” in the abstract setting of a Hilbert space. In this paper, we derive a similar characterization under slightly more general conditions. This is specialized to the finite-dimensional case, and applied to a few well-known problems, including the ν-spline (a piecewise polynomial spline in tension) and near-interpolation, as well as interpolation and smoothing. In particular, one of the main objectives in this paper is to show that the ν-spline is actually a mixed spline, an observation that we believe was not known prior to this work. We also show that the ν-spline is a limiting case of smoothing splines as certain weights increase to infinity, and a limiting case of near-interpolants as certain tolerances decrease to zero. We conclude with an iteration used to construct curvature-bounded ν-spline curves.

Citation Information
Scott N. Kersey. "Mixed Interpolating-Smoothing Splines and the V-Spline" Journal of Mathematical Analysis and Applications Vol. 322 Iss. 1 (2006) p. 28 - 40 ISSN: 0022-247X
Available at: http://works.bepress.com/scott_kersey/22/