Approximation by smoothing variational vector splines for noisy data

B Ivariate Approximation by Discrete Smoothing Pde Splines

This paper deals with the construction and characterization of discrete PDE splines. For this purpose, we need a PDE equation (usually an elliptic PDE), certain boundary conditions and a set of points to approximate. We give two results about the convergence of a discrete PDE spline to a function of a fixed space in two different cases: (1) when the approximation points are fixed; (2) when the ...

Nonparametric fixed-interval smoothing with vector splines

Approximation of Vector Fields by Thin Plate Splines with Tension

We study a vectorial approximation problem based on thin plate spline with tension involving two positive parameters one for a control of the oscillations and the other one allows a control on the divergence and rotational components of the field. The existence and uniqueness of the solution is proved and the solution is explicitly given. We study the limit problems and the convergence problem ...

Approximating data with weighted smoothing splines∗

Given a data set (ti, yi), i = 1, . . . , n with the ti ∈ [0, 1] non-parametric regression is concerned with the problem of specifying a suitable function fn : [0, 1] → R such that the data can be reasonably approximated by the points (ti, fn(ti)), i = 1, . . . , n. If a data set exhibits large variations in local behaviour, for example large peaks as in spectroscopy data, then the method must ...

Multivariate Splines for Data Fitting and Approximation

Methods for scattered data fitting using multivariate splines will be surveyed in this paper. Existence, uniqueness, and computational algorithms for these methods, as well as their approximation properties will be discussed. Some applications of multivariate splines for data fitting will be briefly explained. Some new research initiatives of scattered data fitting will be outlined. §