Showing papers on "Monotone cubic interpolation published in 1986"
TL;DR: In this article, a rational spline alternative to the spline under-tension is proposed for shape-preserving interpolation, and its application to shape preserving interpolation is considered.
Abstract: A rational spline alternative to the spline-under-tension is discussed. Its application to shape preserving interpolation is considered.
118 citations
TL;DR: In this article, the existence of monotone and convex splines, having degree n and order of continuity k, which interpolate to a set of data at the knots is investigated.
Abstract: This paper is concerned with the problem of existence of monotone and/or convex splines, having degree n and order of continuity k, which interpolate to a set of data at the knots. The interpolating splines are obtained by using Bernstein polynomials of suitable continuous piecewise linear functions; they satisfy the inequality k < n k. The theorems presented here are useful in developing algorithms for the construction of shape-preserving splines interpolating arbitrary sets of data points. Earlier results of McAllister, Passow and Roulier can be deduced from those given in this paper.
88 citations
TL;DR: This article describes and presents examples of some techniques for the representation and interactive design of surfaces based on a parametric surface representation that user v-spline curves and extends their application to a rectangular grid of control points.
Abstract: This article describes and presents examples of some techniques for the representation and interactive design of surfaces based on a parametric surface representation that user v-spline curves. These v-spline curves, similar in mathematical structure to v-splines, were developed as a more computationally efficient alternative to splines in tension. Although splines in tension can be modified to allow tension to be applied at each control point, the procedure is computationally expensive. The v-spline curve, however, uses more computationally tractable piecewise cubic curves segments, resulting in curves that are just as smoothly joined as those of a standard cubic spline. After presenting a review of v-splines and some new properties, this article extends their application to a rectangular grid of control points. Three techniques and some application examples are presented.
81 citations
TL;DR: In this paper, the optimal order error estimates for three popular derivative-free spline interpolation schemes are developed for the first and last subintervals of the spline matrix.
Abstract: Cubic spline interpolation schemes which require no derivative information at the end points are of great practical importance and have been included in several general purpose software libraries. In this paper optimal order error estimates are developed for three popular schemes of this “derivative free” type. The approximation of $C^1 [a,b]\backslash C^2 [a,b]$ functions by any such “derivative free” method that reproduces cubics, necessarily displays some dependence on the local mesh ratio. However, for the spline interpolants studied here this dependence is restricted to the first and last subintervals.
31 citations
TL;DR: In this article, a class of simple rational splines and their application to monotonic interpolation was considered and a selection of numerical results was presented in Figs. 4 and 11.
Abstract: We shall consider a class of simple rational splines and their application to monotonic interpolation to monotonic data. Our method is situated between interpolation with the usual cubic splines and with monotone quadratic splines. A selection of numerical results is presented in Figs. 4–11.
12 citations
TL;DR: In this article, the authors developed a new approach to the problem of real-time interpolation of digital signals using local cubic polynomial interpolative routines known as cubic spline functions.
Abstract: Deals with the development of a new approach to the problem of real-time interpolation of digital signals. Whereas the traditional methods of performing this operation make use of digital filters (FIR or IIR), this approach utilizes local cubic polynomial interpolative routines known as cubic spline functions. By using cubic splines, an algorithm has been obtained which can be implemented in a simple and economical way, yielding the desired real-time interpolator. The properties of this system include conceptual and structural simplicity, local control, speed of operation, and versatility.
11 citations
01 Jan 1986
TL;DR: A submitted manuscript is the version of the article upon submission and before peer-review as discussed by the authors, while a published version is the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
6 citations
Journal Article•
5 citations
TL;DR: Errors in spline and Lagrangian methods of interpolation are compared for a range of functions, tabular intervals, and levels of data errors as discussed by the authors, and it is shown that for large step-sizes and fairly accurate data Lagrangians are considerably more accurate than splines.
4 citations
TL;DR: A cubic spline method for the numerical solution of a two-point boundary value problem posed on an infinite interval involving a second-order linear differential equation is described in this article, where the stability of the method is analyzed and the theory is illustrated by solving test examples.
4 citations
01 Dec 1986
TL;DR: In this article, a class of cubic spline minimizing some special functional is investigated. This class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter a < 2.
Abstract: A class of cubic spline minimizing some special functional is investigated. This class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter a < 2. For a = 1/2 natural splines are obtained. For a = -1 the spline minimizing the mean value of the third derivative is obtained. It is shown that this spline has the best convergence order.
TL;DR: For a set of convex data, the authors showed that if the data derives from one of these functions, then the above convexity conditions are verified, and showed that the data is convex enough for the rational quadratic spline interpolation.
TL;DR: In this article, a sharp estimate for the exponential decay rate of the inverse of a diagonally dominant matrix is given, which is used to study the bounded spline interpolation at a bi-infinite knot sequence.
Abstract: A sharp estimate for the exponential decay rate of the inverse of a diagonally dominant matrix is given. This is used to study the bounded spline interpolation at a bi-infinite knot sequence.
10 Oct 1986
TL;DR: A “quintic spline” is derived from a “cubic splines” and has it modified and executed for error analysis and a few examples are executed for comparison.
Abstract: The method applied most frequently in drawing a curve to interpolate a set of given points without spoiling the aim for “shape preserving” is parametrized cubic spline method; however, possibility of producing a bad result on “shape preserving” exists. CATIA system which uses “quintic spline” is not a perfect one. We derive a “quintic spline” from a “cubic spline” and has it modified. Except for the above, we also do the work of error analysis and execute a few examples for comparison.
TL;DR: In this article, the Hermite interpolation polynomials for a function analytic on a disk were derived and shown to converge uniformly to the closed subdisk of the function.
Abstract: We derive a Hermite interpolation formula with remainder for a function analytic on a disk. Given such a function, f, and given a preassigned matrix of nodes Z (all such nodes being in a certain closed subdisk), we show that the sequence of Hermite interpolation polynomials for f associated with Z converges uniformily to f on the closed subdisk.