کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4624227 1339536 2006 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Mixed interpolating–smoothing splines and the ν-spline
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Mixed interpolating–smoothing splines and the ν-spline
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 322, Issue 1, 1 October 2006, Pages 28-40