This paper develops a new family of convexity-preserving splines of order n, hereby entitled the CPn-spline, that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term, and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. ...

in this work the collocation method based on quartic b-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. the error analysis and convergence of presented method is discussed. the method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more equations than there are control point positions. Therefore, four gradients which are the first derivative of a quintic B-spline equation are assigned to the given points. In addition to this method, another method to generate a quintic B-spline curve which passes ...

The paper introduces a new method for flexible spline fitting for copula density estimation. Spline coefficients are penalized to achieve a smooth fit. To weaken the curse of dimensionality, instead of a full tensor spline basis, a reduced tensor product based on sparse grids Zenger (1991) is used. To achieve uniform margins of the copula density, linear constraints are placed on the spline coe...

This paper introduces a new method for three-dimensional (3D) coastal geomorphology reconstruction using differential synthetic aperture interferometry (DInSAR). The new method is based on an integration between fuzzy B-spline algorithm and DInSAR method. DInSAR algorithm is involved two parts: (i) 3D map simulation which is based on interferogram simulation and (ii) satellite orbit parameters....

In this work, the relationship between splines and the linear control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical...

Multivariate spline functions are smooth piecewise polynomial functions over triangulations consisting of n-simplices in the Euclidean space IR. A straightforward method for using these spline functions to fit given scattered data and numerically solve elliptic partial differential equations is presented . This method does not require constructing macro-elements or locally supported basis funct...

Bivariate splines with various degrees are considered in this paper. A matrix form of the extended smoothness conditions for these splines is presented. Upon this form, the multivariate spline method for numerical solution of partial differential equations (PDEs) proposed by Awanou, Lai, and Wenston in [The multivariate spline method for scattered data fitting and numerical solutions of partial...

Accurate estimation of an underlying function and its derivatives is one of the central problems in statistics. Parametric forms are often proposed based on the expert opinion or prior knowledge of the underlying function. However, these strict parametric assumptions may result in biased estimates when they are not completely accurate. Meanwhile, nonparametric smoothing methods, which do not im...

We describe a method to construct a hierarchical representation of a given implicitly defined algebraic spline curve with the help of weighted spline wavelets. These wavelets are adapted to the region of interest, in our case to the region along the curve, by means of a weighted inner product. The application of two different types of weighted spline wavelets is considered and compared with sta...