Abstract. For the efficient numerical solution of elliptic variational inequalities on closed convex sets, multigrid methods based on piecewise linear finite elements have been investigated over the past decades. Essential for their success is the appropriate approximation of the constraint set on coarser grids which is based on function values for piecewise linear finite elements. On the other...

Introduction 3D reconstruction of an object from its 2D cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. In order to perform 3D reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. Mate...

When applying nonparametric regression methods, the researcher is interested in estimating the relationship between one dependent variable, Y , and one or several covariates, X1, . . . , Xq. We discuss here the situation with one covariate, X (the case with multiple covariates is addressed in the references provided below). The relationship between X and Y can be expressed as the conditional ex...

Univariate and multivariate quadratic spline quasi-interpolants provide interesting approximation formulas for derivatives of approximated functions that can be very accurate at some points thanks to the superconvergence properties of these operators. Moreover, they also give rise to good global approximations of derivatives on the whole domain of definition. From these results, some collocatio...

Abstract: In this paper a family of numerical methods is developed for solution of non-linear sixth-order two-point boundary-value problems using parametric septic spline. It is shown that the new methods give approximations, which are better than existing spline methods. End equations of the spline are derived and truncation error is given. Convergence analysis is discussed through standard pr...

introduction relative dose computation is a necessary step in radiation treatment planning. therefore, finding an approach that is both fast and accurate seems to be necessary. the purpose of this work was to investigate the feasibility of natural cubic spline to reconstruct dose maps for linear accelerator radiation treatment fields in comparison with those of the simulation. materials and met...

In nonrigid motion analysis, deformation fields are often modeled using splines defined on a control-point grid. Inspired by recent development of meshfree methods, we propose a novel motion model that does not use control-point grids, nor use explicit node connections. We also propose a regularizer for the deformation field and the minimization algorithm. The method has promising features such...

The non-local hyperbolic partial differential equations have many applications in sciences and engineering. A collocation finite element approach based on exponential cubic B-spline and quintic B-spline are presented for the numerical solution of the wave equation subject to nonlocal boundary condition. Von Neumann stability analysis is used to analyze the proposed methods. The efficiency, accu...