Monotone cubic interpolation

About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.

Interpolation by cubic splines on triangulations

Abstract: We describe an algorithm for constructing point sets which admit unique Lagrange and Hermite interpolation from the space S 1 3 (() of C 1 splines of degree 3 deened on a general class of triangulations. The triangulations consist of nested polygons whose vertices are connected by line segments. In particular, we have to determine the dimension of S 1 3 (() which is not known for arbitrary triangulations. Numerical examples are given. x1. Introduction In the literature, point sets which admit unique Lagrange and Hermite interpolation from spaces S r q (() of splines of degree q and smoothness r were constructed for crosscut partitions , in particular for 1-and 2-partitions. Results on the approximation order of these interpolation methods were also proved. (Because of space limitations, we refer to the references of our paper 5] in this volume.) Hermite interpolation schemes for S 1 q ((); q 5, where is an arbitrary triangulation, were given in 1, 3]. An inductive method for constructing Lagrange and Hermite interpolation points for S 1 q ((); q 5, where is an arbitrary triangulation, was developed in 2]. Here, in each step, one vertex is added to the subtriangulation considered before. For q = 4, this method works under certain assumptions on. The most complex case is q = 3, since even the dimension of S 1 3 (() is not known for arbitrary triangulations. In this paper, we develop Lagrange and Hermite interpolation methods for S 1 3 ((). The triangulations consist of nested polygons whose vertices are connected in a natural way. The interpolation points are constructed inductively by passing through the vertices of the nested polygons, where in contrast to 2], the choice of these vertices is unique. All rights of reproduction in any form reserved.

Deficient Discrete Quartic Spline Interpolation

Abstract: In the present paper, the existence, uniqueness and convergence properties of discrete quartic spline interpolation over non-uniform mesh have been studied which match the given functional values at mesh points, interior points and second difference at boundary points.

A generalized bootstrap method to determine the yield curve

Abstract: A new technique is described for operationalizing the bootstrap methodology to estimate the yield curve given any available data set of bond yields. The problem of missing data points is dealt with using symbolic cubic spline interpolation. To make such an approach tractable the computer algebra system Maple is employed to symbolically generate the interpolation equations for the missing data points and to solve the nonlinear equation system in order to obtain the points on the yield curve. Several examples with real data demonstrate the usefulness of the methodology.