Journal ArticleDOI
Computation of Smoothing and Interpolating Natural Splines via Local Bases
Tom Lyche,Larry L. Schumaker +1 more
TLDR
In this paper, it is shown how smoothing splines can be represented in terms of a local basis, and that the coefficients can be obtained by solution of a banded linear system.Abstract:
It is shown how smoothing splines can be represented in terms of a local basis, and that the coefficients can be obtained by solution of a banded linear system. Recursion relations are developed which permit rapid and accurate calculation of the necessary basis elements.read more
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Book
Aggregation Functions: A Guide for Practitioners
TL;DR: A broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums.
Journal ArticleDOI
Cubic splines for image interpolation and digital filtering
Hsieh Hou,H. Andrews +1 more
TL;DR: Applications to image and signal processing include interpolation, smoothing, filtering, enlargement, and reduction, and experimental results are presented for illustrative purposes in two-dimensional image format.
Journal ArticleDOI
A fortran package for generalized, cross-validatory spline smoothing and differentiation
TL;DR: A subroutine package is presented in which the amount of smoothing on a set of n noisy datapoints is determined from the data by means of the Generalized Cross-Validation or predicted Mean-Squared Error criteria of Wahba and her collaborators.
Journal ArticleDOI
Splines in Statistics
TL;DR: In this paper, splines are presented as a nonparametric function estimating technique, and the method of cross-validation for choosing the smoothing parameter is discussed and the general multivariate regression/surface estimation problem is addressed.
Journal ArticleDOI
On optimal smoothing and derivative estimation from noisy displacement data in biomechanics
TL;DR: The use of optimally regularized, natural quintic splines for estimating smoothed positions, velocities, and accelerations from equidistantly sampled, noisy position measurements is described.
References
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Journal ArticleDOI
Smoothing by spline functions. II
TL;DR: In this paper, the authors generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence, which is the same as in this paper.
Journal ArticleDOI
Spline functions and the problem of graduation.
TL;DR: The aim of this note is to extend some of the recent work on spline interpolation so as to include also a solution of the problem of graduation of data and the qualitative aspects of the new method are described.