The notion of complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines. To derive properties of complex B-splines in R, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional simplices △∞. Based on this generalization several identities of mu...

The paper presents a method of construction of tight frames for L(Ω), Ω ⊂ R. The construction is based on local orthogonal matrix extension of vectors associated with the transition matrices across consecutive resolution levels. Two explicit constructions are given, one for linear splines on triangular polygonal surfaces with arbitrary topology and the other for quadratic splines associated wit...

Abstract Locally refined B-spline (LRB) surfaces provide a representation that is well suited to scattered data approximation. When set has local details in some areas and largely smooth elsewhere, LR B-splines allow the spatial distribution of degrees freedom follow variations set. An LRB surface approximating where accuracy does not meet required tolerance. In this paper we address, systemati...

In computational dealings with splines, the question of representation is of primary importance. For splines of fixed order on a fixed partition, this is a question of choice of basis, since such splines form a linear space. Only three kinds of bases for spline spaces have actually been given serious attention; those consisting of truncated power functions, of cardinal splines, and of B-splines...

In science and engineering there often is a need for the approximation of scattered multi-dimensional data. A class of powerful scattered data approximators are the multivariate simplex B-splines. Multivariate simplex B-splines consist of Bernstein basis polynomials that are defined on a geometrical structure called a triangulation. Multivariate simplex B-splines have a number of advantages ove...

Employing discrete B-splines instead of the Gaussian distribution, we construct an algorithm for the analysis of ionmobility spectrometry profiles. The algorithm is suitable for hardware implementation because the discrete B-splines are supported by a simple digital filter to compute their weighted sum and their correlations with a given signal. Minutely shifted discrete B-splines are deployed ...

This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type difference penalty with B-splines (HB-splines), were recently introduced the authors as generalization P-splines. HB-splines are bell-shaped basis functions consisting segments made real exponentials eαx,e−αx and linear mu...

We consider solitary wave solutions of the generalized equal width (GEW) wave equation ut + εuux − δuxxt = 0. This paper presents a collocation method for the GEW equation, which is classified as a nonlinear PDE using quadratic B-splines at midpoints as element shape functions. In this research, the scheme of the equation under investigation is found to be unconditionally stable. Test problems ...