A general setting for constrained Z,1-approximation is presented. Let Un be a finite dimensional subspace of C[a, b] and L be a linear operator from Un to C(K) (r = 0, 1) where K is a finite union of disjoint, closed, bounded intervals. For v , u e C(K) with v < u, the approximating set is Univ, u) = {p e Un : v < Lp < u on K} and the norm is \\f\\w = Xf \f\wdx where w a positive continuous fun...

Biquadratic (bi-2) splines are the simplest choice for converting a regular quad meshes into smooth tensor-product spline surfaces. Existing methods for blending three, five or more such bi-2 spline surfaces using surface caps consisting of pieces of low polynomial degree suffer from artifacts ranging from flatness to oscillations. The new construction, based on reparameterization of the bi-2 s...

In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer ) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence an...

A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve lies inside the convex hull of the control points, and the segments of the broken line connecting the control points are tangent to the curve. To construct the...

‎in this paper we introduce a numerical approach that solves optimal control problems (ocps)‎‎using collocation methods‎. ‎this approach is based upon b-spline functions‎.‎the derivative matrices between any two families of b-spline functions are utilized to‎‎reduce the solution of ocps to the solution of nonlinear optimization problems‎.‎numerical experiments confirm our theoretical findings‎.

We propose a fractional spline method for solving differential equations subject to initial conditions. Using the Caputo integral and derivative have construct interpolation with polynomial coefficients. For given function, error bounds were studied stability analysis was completed. The numerical explanation provided considered using three examples. results show that function which interpolates...

This paper considers nonparametric regression to analyze longitudinal data. Some developments of nonparametric regression have been achieved for longitudinal or clustered categorical data. For exponential family distribution, Lin & Carroll [6] considered nonparametric regression for longitudinal data using GEE-Local Polynomial Kernel (LPK). They showed that in order to obtain an efficient estim...

We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions Fourier samples ground truth up a maximum cutoff frequency Kc. The reconstruction task is specified as an optimization with total-variation (TV) regularization (in sense measures) involving Mth order derivative operat...

Three types of spherical splines are presented as developed in the recent literature on constructive approximation, with a particular view towards global (and local) geopotential modeling. These are the tensor-product splines formed from polynomial and trigonometric B-splines, the spherical splines constructed from radial basis functions, and the spherical splines based on homogeneous Bernstein...

The problem of semi-cardinal spline interpolation was solved by Schoenberg exploiting the piecewise polynomial form of the splines. In the present paper, we propose a new construction for the Lagrange functions of semi-cardinal spline interpolation , based on a radial basis and Fourier transform approach. This approach suggests a way of extending semi-cardinal interpolation to polyharmonic spli...