in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...

This paper compares two techniques for the approximation of the offsets to a given planar curve. The two methods are based on approximate conversion of the planar curve into circular splines and Pythagorean hodograph (PH) splines, respectively. The circular splines are obtained using a novel variant of biarc interpolation, while the PH splines are constructed via Hermite interpolation of C boun...

We obtain an estimate for the convergence rate of approximation functions on a differentiable manifold consider two approaches to such functions. The first is based approximate relations and independent given set plane approximations. second approximations in plane. Courant type n-dimensional sphere, projective space, also Zlamal interpolation splines.

Penalized splines have gained much popularity as a flexible tool for smoothing and semi-parametric models. Two approaches have been advocated: 1) use a B-spline basis, equally-spaced knots and difference penalties (Eilers and Marx, 1996) and 2) use truncated power functions, knots based on quantiles of the independent variable and a ridge penalty (Ruppert, Wand and Carroll, 2003). We compare th...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...

Splines in tension are smooth interpolation surfaces whose behavior in unconstrained regions is controlled by the tension parameter. I show that such surfaces can be efficiently constructed with recursive filter preconditioning and introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

A fuzzy if-then rule base may be viewed as a partial function between universes of fuzzy sets. We show how this partial function determines a total one by means of the method of smooting splines. To this end, we identify the fuzzy sets with elements of a finite-dimensional real parameter space in an approximate way, using Perfilieva’s fuzzy transforms.