In this paper results from a forthcoming paper are presented concerning the convexity of multivariate spline functions built from B patches Conditions are given under which it is possible to de ne a control net for such spline functions The control net is understood as a piecewise linear function If it is convex then so is the underlying spline

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

Non-uniform B-spline dictionaries on a compact interval are discussed. For each given partition, dictionaries of B-spline functions for the corresponding spline space are constructed. It is asserted that, by dividing the given partition into subpartitions and joining together the bases for the concomitant subspaces, slightly redundant dictionaries of Bsplines functions are obtained. Such dictio...

The paper investigates new robust code constructions based on bent functions and spline–wavelet transformation. Implementation of in construction increases the probability error detection data channel cryptographic devices. Meanwhile, use spline wavelet theory for constructing codes gives possibility to increase system security from actions an attacker. Presented combine spline-wavelets functio...

To de ne spline subdivision schemes for general compact sets we use the representation of spline subdivision schemes in terms of repeated averages and replace the usual average convex combination by a binary averaging operation between two compact sets introduced in and termed here the metric average These schemes are shown to converge in the Hausdor metric and to provide O h approximation x In...

B-spline functions play important roles in both mathematics and engineering. To describe a numerical method for solving the boundary value problem of linear ODE with second-order by using B-spline. First, the cubic B-spline basis functions are introduced, then we use the linear combination of cubic B-spline basis to approximate the solution. Finally, we obtain the numerical solution by solving ...

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree...