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...

B-splines can be used to approximate data in a variety of metrology applications. In general, the approximation is carried out so as to minimize a criterion deened in terms of the least squares norm. However, often this choice of norm is inappropriate , and a measure such as thè 1 or minimax norm should be chosen. In this tutorial paper, we introduce the topic of B-splines, and we discuss the a...

‎In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets‎. ‎The method combines implicit collocation with the multi-scale method‎. Using the multi-scale method‎, ‎SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain‎. ‎The stability and c...

Powell–Sabin B-splines are enjoying an increased use in the analysis of solids and fluids, including fracture propagation. However, B-spline interpolation does not hold Kronecker delta property and, therefore, imposition Dirichlet boundary conditions is as straightforward for standard finite elements. Herein, we discuss applicability various approaches developed to date weak analyses which empl...

This paper presents an alternative to the semi-orthogonal spline wavelets classically used for multiresolution representation in the eld of computer aided design. This new approach involves less computation, is more modular, and is potentially more exible than the classical approach. This multiresolution scheme is presented through the use of HB-splines, a speciic subset of particular B-splines...

Powell-Sabin splines are C-continuous quadratic splines defined on an arbitrary triangulation. Their construction is based on a particular split of each triangle in the triangulation into six smaller triangles. In this article we give an overview of the properties of Powell-Sabin splines in the context of computer aided geometric design. These splines can be represented in a compact normalized ...