Journal ArticleDOI
Convex interval interpolation with cubic splines, II
Reads0
Chats0
TLDR
In this paper, a necessary and sufficient criterion is presented under which the convex interval interpolation with cubicC1-splines has at least one solution, and an algorithm is given as an algorithm which turns out to be effective.Abstract:
A necessary and sufficient criterion is presented under which the problem of the convex interval interpolation with cubicC1-splines has at least one solution. The criterion is given as an algorithm which turns out to be effective.read more
Citations
More filters
Journal ArticleDOI
Shape Preserving Approximations by Polynomials and Splines
TL;DR: A review of shape preserving approximation methods and algorithms for approxi- mating univariate functions or discrete data is given in this article, where special stress is put on shape preserving interpolation methods by polynomials and splines.
Journal ArticleDOI
An always successful method in univariate convex C 2 interpolation
Jochen W. Schmidt,Walter Heß +1 more
TL;DR: In this paper, the authors considered convex interpolation with variable knots and proposed a staircase algorithm to provide computable intervals for the added knots such that all knots from these intervals allow convexity preserving spline interpolation.
Journal ArticleDOI
Determination of shape preserving interpolants with minimal curvature via dual programs
TL;DR: On etudie, du point de vue numerique, quelques problemes de programmation lies a l'interpolation par fonction spline preservant la convexite ou la monotonie as mentioned in this paper.
Journal ArticleDOI
Convexity preserving interpolation with exponential splines
W. Hess,Jochen W. Schmidt +1 more
TL;DR: In order to select one of the interpolants, by means of a well-known objective function a quadratic optimization problem is stated which can be solved effectively by passing to a dual program.
Journal ArticleDOI
Staircase algorithm and construction of convex spline interpolants up to the continuity C3
TL;DR: Based on the staircase algorithm, several methods are presented which allow the construction of convex spline interpolants up to the continuity C 3 .
References
More filters
Book
A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
Journal ArticleDOI
Monotone Piecewise Cubic Interpolation
F. N. Fritsch,R. E. Carlson +1 more
TL;DR: In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.
Journal ArticleDOI
Spline functions and the problem of graduation.
TL;DR: The aim of this note is to extend some of the recent work on spline interpolation so as to include also a solution of the problem of graduation of data and the qualitative aspects of the new method are described.
Journal ArticleDOI
de Boor, C., A Practical Guide to Splines. Applied Mathematical Sciences 27. Berlin‐Heidelberg‐New York, Springer‐Verlag 1978. XXIV, 392 S., DM 32,50. US $ 17.90
Journal ArticleDOI
Monotone and convex spline interpolation
Eli Passow,John A. Roulier +1 more
TL;DR: For a set of monotone (and/or convex) data, this article considered the possibility of finding a spline interpolant, of pre-determined smoothness, which is either monotonicity or convex.