Paper Info
Title
Fitting Dense and Sparse Reduced Data.
Abstract
This paper addresses the topic of fitting reduced data represented by the sequence of interpolation points (mathcal{M}={q_i}_{i=0}^n) in arbitrary Euclidean space (mathbb {E}^m). The parametric curve (gamma ) together with its knots (mathcal{T}={t_i}_{i=0}^n) (for which (gamma (t_i)=q_i)) are both assumed to be unknown. We look at some recipes to estimate (mathcal{T}) in the context of dense versus sparse (mathcal{M}) for various choices of interpolation schemes (hat{gamma }). For (mathcal{M}) dense, the convergence rate to approximate (gamma ) with (hat{gamma }) is considered as a possible criterion to force a proper choice of new knots (hat{mathcal{T}}={hat{t}_i}_{i=0}^n approx mathcal{T}). The latter incorporates the so-called exponential parameterization “retrieving” the missing knots (mathcal{T}) from the geometrical spread of (mathcal{M}). We examine the convergence rate in approximating (gamma ) by commonly used interpolants (hat{gamma }) based here on (mathcal{M}) and exponential parameterization. In contrast, for (mathcal{M}) sparse, a possible optional strategy is to select (hat{mathcal{T}}) which optimizes a certain cost function depending on the family of admissible knots (hat{mathcal{T}}). This paper focuses on minimizing “an average acceleration” within the family of natural splines (hat{gamma }=hat{gamma }^{NS}) fitting (mathcal{M}) with (hat{mathcal{T}}) admitted freely in the ascending order. Illustrative examples and some applications listed supplement theoretical component of this work.
Year
DOI
Venue
2018
10.1007/978-3-030-03314-9_1
ACS
Field
DocType
Citations 
Discrete mathematics,Parametric equation,Exponential function,Euclidean space,Rate of convergence,Knot (unit),Mathematics
Conference
0
PageRank 
References 
Authors
0.34
6
2
Name
Order
Citations
PageRank
Ryszard Kozera116326.54
Artur Wilinski221.11