This paper presents a simple and fast recurrence equation-based method for solving the cubic spline interpolation problem. The computational complexity of the method is O(n), where n is the number of measurements. The recurrence equation-based method is illustrated by an example that estimates the movement of a moving object. The paper also describes a MATLAB implementation of the new method an...

By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus eecient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coeecients allow a characterization of the underlying Hilbert space struc...

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

as a function of s at the k+ 1 points ti, . . . , ti+k. The elements of $k,t are called polynomial splines of order k with knot sequence t. Let τ := (τi) n 1 be a strictly increasing real sequence. As is shown in [12], there exists, for given f , exactly one s ∈ $k,t, such that s(τi) = f(τi), i = 1, . . . , n, if and only if Ni,k(τi) 6= 0, i = 1, . . . , n, i.e., if and only if ti < τi < ti+k, ...

We study the reconstruction of cardinal splines f(t), from their average samples yn = f ∗h(n), n ∈ Z, when the average function h(t) has support in [−1/2, 1/2]. We investigate the existence and uniqueness of the solution of the following problem: for given dates yn, find a cardinal spline f(t), of a given degree, satisfying yn = f ∗ h(n), n ∈ Z. 1 Spline interpolation and average sampling First...

We show that the Lp( )-norm of the error in surface spline interpolation of a compactly supported function in the Sobolev space W 2m 2 decays like O( p) where p := minfm;m+ d=p d=2g and m is a parameter related to the smoothness of the surface spline. In case 1 p 2, the achieved rate of O( ) matches that of the error when the domain is all of R and the interpolation points form an in nite grid.