We bound the dimension of xed degree real algebraic interpolatory spline spaces. For a given planar triangulation T real algebraic splines interpolate speciied zi values at the vertices vi = (xi; yi) of T. For a three dimensional simplicial complex ST , real algebraic splines interpolate the boundary vertices vj = (xj; yj; zj) of ST. The main results of this paper are lower bounds on the dimens...

In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local vari...

The construction of weighted extended B-splines (web-splines), as recently introduced by the authors and J. Wipper for uniform knot sequences, is generalized to the nonuniform case. We show that web-splines form a stable basis for splines on arbitrary domains in R which provides optimal approximation power. Moreover, homogeneous boundary conditions, as encountered frequently in finite element a...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (J. Roy. Statist. Soc. Set. B 40 (1978) 364-372; 45 (1983) 133-150) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local...

Abstract Multivariate basis splines (B‐splines) and Non‐uniform rational B‐splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical (THB‐splines) provide a solution for this. THB‐splines organize the parameter space into structure, which enables efficient approximation representation of functions with different levels detail. The truncation mechanism ensures...

Introduction: The Shallow Radar instrument (SHARAD) on the Mars Reconnaissance Orbiter (MRO) has been successful at penetrating into icy deposits [1-3], but most of the rocky units are opaque to SHARAD. The main exceptions to this are the youngest major volcanic surfaces, Cerberus Fossae 2 and 3 units and Amazonis Planitia 2 north unit [4]. We suggest that these units have low radar loss becaus...

Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators , and present a generalized Hermite-Genochi formula. This formula then allows the definition of a larger class of fractional B-splines.

In this paper we consider polynomial splines with equidistant nodes which may grow as O|x|. We present an integral representation of such splines with a distribution kernel where exponential splines are used as basic functions. By this means we characterize splines possessing the property that translations of any such spline form a basis of corresponding spline space. It is shown that any such ...

Tile $\mathrm{B}$-splines in $\mathbb R^d$ are defined as autoconvolutions of indicators tiles, which special self-similar compact sets whose integer translates tile the space R^d$. These functions not piecewise-polynomial, however, being direct generalizations classical $\mathrm{B}$-splines, they enjoy many their properties and have some advantages. In particular, exact values Hölder exponents...