Data measuring and further processing is the fundamental activity in all branches of science technology. interpolation has been an important part computational mathematics for a long time. In paper, we are concerned with by polyharmonic splines arbitrary dimension. We show connection this radial basis functions smooth generating functions, which provide means minimizing L2 norm chosen derivativ...

In this paper, geometric interpolation by G cubic spline is studied. A wide class of sufficient conditions that admit a G cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the ...

Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem. However, this method has been associated with very high computational cost, as compared to alternative methods such as finite element or multivariate spline interpolation. For example, the direct evaluation at M locations of a radial b...

Abstract. In this paper we propose a local spline method for the approximation of the derivative of a function f . It is based on an optimal spline quasi-interpolant operator Q2, introduced in [12]. Differentiating Q2 f , we construct the pseudo-spectral derivative at the quasi-interpolation knots and the corresponding differentiation matrix. An error analysis is proposed. Some numerical result...

In polynomial and spline interpolation the k-th derivative of the interpolant, as a function of the mesh size h, typically converges at the rate of O(hd+1−k) as h → 0, where d is the degree of the polynomial or spline. In this paper we establish, in the important cases k = 1, 2, the same convergence rate for a recently proposed family of barycentric rational interpolants based on blending polyn...

In this paper, we present an easy and e cient method for computing the range of a function by using spline quasi-interpolation. We exploit the close relationship between the spline function and its control polygon and use tight subdivision technique in order to obtain monotonic splines which make the range of the spline easy to compute. The proposed method is useful in case of given scattered d...

We show that if the open, bounded domain Ω ⊂ Rd has a sufficiently smooth boundary and if the data function f is sufficiently smooth, then the Lp(Ω)-norm of the error between f and its surface spline interpolant is O(δγp+1/2) (1 ≤ p ≤ ∞), where γp := min{m,m − d/2 + d/p} and m is an integer parameter specifying the surface spline. In case p = 2, this lower bound on the approximation order agree...

Classical Cubic spline interpolation needs to solve a set of equations of high dimension. In this work we show how to compute the interpolant using a FIR digital filter, with a reduced number of operations per interpolated point and high accuracy. Additionally, the computation can be made on real time as the signal samples are acquired. Following this approach, we show how to obtain easily the ...