Construction of Approximation Functionals for Minimal Splines

Construction of Images Using Minimal Splines

Tasks of data compression, transmission, subsequent recovery with a given accuracy are of great practical importance. In this paper we consider a problem of constructing graphical information on a plane with the help of a parametric defined splines with different properties. Here we compare the polynomial and the trigonometric splines of the first and the second order, the polynomial integro-di...

Approximation by Conic Splines

We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε +O(1), if the spline consists of parabolic arcs, and c2ε + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We also show that...

Approximation Orders for Natural Splines in Arbitrary

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. §

Bivariate segment approximation and splines

The problem to determine partitions of a given reet angle which are optimal for segment approximation (e.g. by bivariate pieeewise polynomials) is investigated. We give eriteria for optimal partitions and develop algorithms for eomputing optimal partitions of eertain types. It is shown that there is a surprising relationship between various types of optimal partitions. In this way, we obtain go...