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...

Root lattices are efficient sampling lattices for reconstructing isotropic signals in arbitrary dimensions, due to their highly symmetric structure. One root lattice, the Cartesian grid, is almost exclusively used since it matches the coordinate grid; but it is less efficient than other root lattices. Box-splines, on the other hand, generalize tensor-product B-splines by allowing non-Cartesian ...

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...

We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. x1. Introduction Suppose we are given values ff(v)g v2V of an unknown function f at a set V of scattered points in IR 2. To approximate f, we choose a linear space S of polynomial splines of degree d deened on a triangulation 4 with vertices at the points of V. be the set of...

We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. x1. Introduction Suppose we are given values ff(v)g v2V of an unknown function f at a set V of scattered points in IR 2. To approximate f, we choose a linear space S of polynomial splines of degree d deened on a triangulation 4 with vertices at the points of V. be the set of...

In this paper, planar parametric Hermite cubic interpolants with small curvature variation are studied. By minimization of an appropriate approximate functional, it is shown that a unique solution of the interpolation problem exists, and has a nice geometric interpretation. The best solution of such a problem is a quadratic geometric interpolant. The optimal approximation order 4 of the solutio...