The algorithms and programs in this handy book deal almost exclusively with cubic splines. A short introduction stresses the maximum "smoothness" of "natural" splines. The next chapter reviews the numerical solution of tridiagonal linear systems by Gauss elimination and of block tridiagonal linear systems by relaxation. Chapter 3 offers programs for cubic spline interpolation with various (sepa...

Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

We study how to use bivariate splines for scattered data interpolation and fitting with preservation of non-negativity of the data values. We propose a minimal energy method to find a C1 smooth interpolation/fitting of non-negative data values from scattered locations based on bivariate splines. We establish the existence and uniqueness of the minimizer under mild assumptions on the data locati...

A measurement method of the three-dimensional electromagnetic articulograph system is presented to investigate the dynamic behavior of articulatory organs which can include lateral or rotational movements. To accurately represent the spatial pattern of the magnetic field, we use a multivariate B-spline function, which smoothly interpolates a given set of calibration data samples. The strength o...

The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order (1 ≤ p ≤ ∞) of interpolatio...