The construction of range restricted univariate and bivariate interpolants to gridded data is considered. We apply Gregory’s rational cubic C splines as well as related rational quintic C splines. Assume that the lower and upper obstacles are compatible with the data set. Then the tension parameters occurring in the mentioned spline classes can be always determined in such a way that range rest...

In this project, I will introduce a method to estimate the function by cubic splines. As an example, I will focus on the non-homogeneous Poisson process. Since this method uses an optimization model based on the maximum likelihood principle, it may applied to other stochastic processes. The most critical point of this presentation is a nonnegativity constriant on the splines. In addition, choos...

A general setting is given for smooth interpolating splines depending on a parameter such that as this parameter approaches infinity the spline converges to the piecewise linear interpolant. The theory includes the standard exponential spline in tension, a rational spline, and several cubic splines. An algorithm is given for one of the cubics; the parameter for this example controls the spacing...

We analytically investigate univariate C continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computa...

In the present paper, we give approximate values of π deduced from the areas of inscribed and circumscribed quadratic and cubic circular splines. Similar results on circular splines of higher degrees and higher approximation orders can be obtained in the same way. We compare these values to those obtained by computing the perimeters of those circular splines. We observe that the former are much...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...