$T_{f}$-splines et approximation par $T_{f}$ -prolongement

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...

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...

Convex Approximation by Quadratic Splines

Given a convex function f without any smoothness requirements on its derivatives, we estimate its error of approximation by C 1 convex quadratic splines in terms of ! 3 (f; 1=n).

On uniform approximation by splines

for 0 ≤ r ≤ k − 1. In particular, dist (f, S π) = O(|π| ) for f ∈ C(I), or, more generally, for f ∈ C(I), such, that f (k−1) satisfies a Lipschitz condition, a result proved earlier by different means [2]. These results are shown to be true even if I is permitted to become infinite and some of the knots are permitted to coalesce. The argument is based on a “local” interpolation scheme Pπ by spl...

Les maladies causées par Clostridium perfringens et Cl. novyi