A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.

This tutorial paper addresses the problem of high-quality resizing that is arbitrary-scale conversion of images cast as projection of the underlying function on spline-like spaces. Such spaces are determined by the corresponding bases, which fully determine the quality of scale conversion. In our setting, the spacegenerating functions are chosen from the class of piecewise (spline-based) basis ...

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 explores the possibilities of point cloud reduction using  insensitive support vector regression (-SVR).  -SVR is a technique that can carry out the regression using different kernel functions (sigmoid, radial basis function, B-spline, spline, etc.) and it is suitable for detection of flat regions and regions with high curvature in scanned data. Using  -SVR the density of preserv...

For spline smoothing one can rewrite the smooth estimation as a linear mixed model (LMM) where the smoothing parameter appears as the variance of spline basis coefficients. Smoothing methods that use basis functions with penalization can utilize maximum likelihood (ML) theory in LMM framework ([8]). We introduce the minimum description length (MDL) model selection criterion in LMM and propose a...

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support, using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal s...

This paper investigates the mathematical background of multiresolution analysis in the specific context where the signal is represented by irregularly sampled data at known locations. The study is related to the construction of nested piecewise polynomial multiresolution spaces represented by their corresponding orthonormal bases. Using simple spline basis orthonormalization procedures involves...

The usefulness of fuzzy input fuzzy output functions and their interpolation/approximation by different operators in fuzzy control motivate their deeper theoretical study. We obtain some properties of fuzzy B-spline series such as variation and uncertainty diminishing property. We also propose spline approximation of fuzzy input fuzzy output functions. Key–Words: Fuzzy numbers, Fuzzy splines, A...