Given a point configuration A, we uncover connection between polynomial-reproducing spline spaces over subsets of conv(A) and fine zonotopal tilings the zonotope Z(V) associated to corresponding vector configuration. This link directly generalizes known result on Delaunay configurations naturally encompasses, due its combinatorial character, case repeated affinely dependent points in A. We prov...

Most of the fundamental theories and mathematical models engineering physical sciences are expressed in terms partial differential equations (PDEs). Several studies were carried out for numerical approximation second order linear Klein-Gordon equation. This study constructed a new technique The scheme was based on employing non-polynomial cubic spline method (NPCSM). time derivatives involved e...

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method (FEM). While identical to FEM with Nédélec’s basis functions in the lowest order case, it is based on B-spline and NonUniform Rational B-spline...

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...

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...

Best L1 approximations of the Heaviside function in Chebyshev and weak-Chebyshev spaces has a Gibbs phenomenon. It has been shown in the nineties for the trigonometric polynomial [1] and polygonal line cases [2]. By mean of recent results of characterization of best L1 approximation in Chebyshev and weak-Chebyshev spaces [3] that we recall, this Gibbs phenomenon can also be evidenced in the pol...

The polynomial space H in the span of the integer translates of a box spline M admits a well-known characterization as the joint kernel of a set of homogeneous differential operators with constant coefficients. The dual space H∗ has a convenient representation by a polynomial space P, explicitly known, which plays an important role in box spline theory as well as in multivariate polynomial inte...