Showing papers on "Monotone cubic interpolation published in 2000"
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01 Jan 2000
TL;DR: In this paper, interpolation by polynomials and Lagrange splines cubic spline interpolation algorithms for computing 1-D and 2-D polynomial splines methods of montone and convex splined interpolation methods of shape-preserving splines interpolation local bases for generalized tension splines are studied.
Abstract: Interpolation by polynomials and Lagrange splines cubic spline interpolation algorithms for computing 1-D and 2-D polynomial splines methods of montone and convex spline interpolation methods of shape-preserving spline interpolation local bases for generalized tension splines GB-splines of arbitrary order methods of shape preserving local spline approximation difference method for construction hyperbolic tension splines discrete generalized tension splines methods of shape preserving parametrization.
114 citations
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TL;DR: A survey of multivariate Lagrange and Hermite interpolation by algebraic polynomials can be found in this article, where the basic concepts and techniques which have been developed in that period of time are presented and illustrated with examples.
90 citations
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TL;DR: In this paper, a survey of the field of interpolation by bivariate splines is presented, where the authors summarize results on the dimension and the approximation order of the spline spaces, and describe interpolation methods for these spaces.
79 citations
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TL;DR: C cubic L 1 splines provide C 1 -smooth, shape-preserving, multiscale interpolation of arbitrary data, including data with abrupt changes in spacing and magnitude, with no need for monotonicity or convexity constraints, node adjustment or other user input.
62 citations
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TL;DR: A new cubic convolution spline interpolation (CCSI) for both one-dimensional and two-dimensional signals is developed in order to subsample signal and image compression data and yields a very accurate algorithm for smoothing.
Abstract: A new cubic convolution spline interpolation (CCSI )for both one-dimensional (1-D) and two-dimensional (2-D) signals is developed in order to subsample signal and image compression data. The CCSI yields a very accurate algorithm for smoothing. It is also shown that this new and fast smoothing filter for CCSI can be used with the JPEG standard to design an improved JPEG encoder-decoder for a high compression ratio.
54 citations
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TL;DR: The degree of smoothness attained is C2 which is more powerful than a previous C1 method and the rational spline scheme has a unique representation.
51 citations
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TL;DR: In this article, a weighted rational cubic spline interpolation has been constructed using the rational cubic interpolation with linear denominator and the rational spline based on function values, and the problems to constrain the weighted rational interpolation curves to lie strictly above or below a given piecewise linear curve and between two given piece-wise linear curves can be solved completely.
48 citations
22 Sep 2000
TL;DR: In this paper, the ephemeris orbit model is approximated by simple curves and piecewise polynomial interpolation is shown to be appropriate for the purpose, and especially splines and Hermite polynomials of different degrees and sampling intervals are compared.
Abstract: In order to speed up satellite position and velocity computation, the ephemeris orbit model is approximated by simple curves. Piecewise polynomial interpolation is shown to be appropriate for the purpose, and especially splines and Hermite polynomials of different degrees and sampling intervals are compared. Cubic Hermite interpolation, along with its other beneficial properties, attains more than tenfold efficiency compared to ephemeris evaluation.
26 citations
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TL;DR: It is shown that under certain conditions on the data, there always exists a convexity preservation C1 cubic spline interpolation if the triangulation is refined sufficiently many times.
22 citations
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TL;DR: The technique is based on Voronoi's algorithm for generating a chain of successive minima in a multiplicative cubic lattice, which is used for calculating the fundamental unit and regulator of a purely cubic number field.
Abstract: The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1 and characteristic at least 5. The technique is based on Voronoi's algorithm for generating a chain of successive minima in a multiplicative cubic lattice, which is used for calculating the fundamental unit and regulator of a purely cubic number field.
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TL;DR: A Newton-type approach is used to deal with bivariate polynomial Hermite interpolation problems when the data are distributed in the intersections of two families of straight lines, as a generalization of regular grids.
Abstract: A Newton-type approach is used to deal with bivariate polynomial Hermite interpolation problems when the data are distributed in the intersections of two families of straight lines, as a generalization of regular grids. The interpolation operator is degree-reducing and the interpolation space is a minimal degree space. Integral remainder formulas are given for the Lagrange case, then extended to the Hermite case, and finally used to obtain error estimates.
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TL;DR: More general and stronger estimations of bounds for the fundamental functions of Hermite interpolation of higher order on an arbitrary system of nodes are given in this article, based on this result conditions for convergence of the Hermite- Fejer-type interpolation and Grunwald type theorems are essentially simplified and improved.
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19 Jul 2000TL;DR: It is attempted that the spline method preserves the shape of the data when it is positive, and the curve scheme under discussion is C/sup 1/.
Abstract: A piecewise rational cubic spline has been introduced to visualize the positive data in its natural form. The article explains how it is attempted that the spline method preserves the shape of the data when it is positive. The spline representation is interpolatory and applicable to the scalar valued data. The shape parameters in the description of the rational cubic have been constrained in such a way that they control the shape of the curve to avoid any noise. As far as visual smoothness is concerned, the curve scheme under discussion is C/sup 1/.
01 Jan 2000
TL;DR: In this paper, an algorithm for constructing Lagrange and Hermite interpolation sets for spaces of cubic C(sup 1)-splines on general classes of triangulations built up of nested polygons whose vertices are connected by line segments is presented.
Abstract: : We develop an algorithm for constructing Lagrange and Hermite interpolation sets for spaces of cubic C(sup 1)-splines on general classes of triangulations built up of nested polygons whose vertices are connected by line segments. Additional assumptions on the triangulation are significantly reduced compared to the special class given in. Simultaneously, we have to determine the dimension of these spaces, which is not known in general. We also discuss the numerical aspects of the method.
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TL;DR: Set of solvability of Hermite multivariate interpolation problems with the sum of multiplicities less than or equal to 2n + 1, where n is the degree of the polynomial space is characterized.
Abstract: In this paper we characterize sets of solvability of Hermite multivariate interpolation problems with the sum of multiplicities less than or equal to 2n + 1, where n is the degree of the polynomial space. This can be viewed as a natural generalization of a well-known result of Severi (1921).
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TL;DR: It is shown that spherical rational quartic curves interpolating such data always exist, and that the family of these curves hasn degrees of freedom for any given Hermite data onSn, n ≥ 2.
Abstract: We study the existence and computation of spherical rational quartic curves that interpolate Hermite data on a sphere, i.e. two distinct endpoints and tangent vectors at the two points. It is shown that spherical rational quartic curves interpolating such data always exist, and that the family of these curves hasn degrees of freedom for any given Hermite data onSn, n ≥ 2. A method is presented for generating all spherical rational quartic curves onSn interpolating given Hermite data.
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TL;DR: In this paper, an eigenvalue analysis of the first-order Hermite cubic spline collocation differentiation matrices with arbitrary collocation points is presented and compared with some other discrete methods, such as finite difference methods.
Abstract: In this paper, we present an eigenvalue analysis of the first-order Hermite cubic spline collocation differentiation matrices with arbitrary collocation points. Some important features are explored and the method is compared with some other discrete methods, such as finite difference methods. A class of spline collocation methods with upwind features is proposed for solving singular perturbation problems.
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TL;DR: In this paper, the problem of semi-cardinal interpolation for polyharmonic splines is considered and a solution to this problem using a Lagrange series representation is presented using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.
Abstract: We consider the problem of semi-cardinal interpolation for polyharmonic splines. For absolutely summable data sequences, we construct a solution to this problem using a Lagrange series representation. The corresponding Lagrange functions are deened using Fourier transforms and the technique of Wiener-Hopf factorizations for semi-space lattices.
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TL;DR: In this article, a singular-ended spline interpolation method based on cubic splines and Overhauser splines is proposed to analyze the dynamic response of a 2D rigid footing interacting with a half-space.
Abstract: A method of interpolation of the boundary variables that uses spline functions associated with singular elements is presented. This method can be used in boundary element method analysis of 2-D problems that have points where the boundary variables present singular behaviour. Singular-ended splines based on cubic splines and Overhauser splines are developed. The former provides C2-continuity and the latter C1-continuity across element edges. The potentialities of the methodology are demonstrated analysing the dynamic response of a 2-D rigid footing interacting with a half-space. It is shown that, for a given number of elements at the soil–foundation interface, the singular-ended spline interpolation increases substantially the displacement convergence rate and delivers smoother traction distributions. Copyright © 2000 John Wiley & Sons, Ltd.
01 Jan 2000
TL;DR: In this paper, a new approach to Hermite subdivision is presented based on the observation that a sequence of second order Hermite data define a unique interpolating cubic C(sup 1) spline.
Abstract: : We present a new approach to Hermite subdivision schemes. It is based on the observation that a sequence of second order Hermite data define a unique interpolating cubic C(sup 1) spline. The B-Spline form of this interpolating spline leads to a stationary binary subdivision scheme with 4 different subdivision rules for the control points. We construct a generalized 4-point scheme which leads to a new family of C(sup 2) Hermite subdivision schemes.
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TL;DR: In this article, the authors review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations, and discuss a few open problems.
Abstract: We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations.
We also discuss a few open problems.
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TL;DR: In this paper, a modified form of surface spline interpolation is proposed which overcomes boundary effects by using only the values of the data function f at the given interpolation points.
Abstract: Surface spline interpolation when the domain is all of R d is known to converge much faster to the data function f than in the case when the domain is the unit ball. This difference is understood to be due to boundary effects which, as will be shown, also affect the size of the surface spline's coefficients. We propose a modified form of surface spline interpolation which, to a great extent, overcomes these boundary effects. This modified surface spline interpolant uses only the values of f at the given interpolation points.
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TL;DR: In this article, a new technique is described for operationalizing the bootstrap methodology to estimate the yield curve given any available data set of bond yields using symbolic cubic spline interpolation.
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.
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TL;DR: In this article, a result due to Gevorgian, Sahakian, and the author concerning the regularity of bivariate Hermite interpolation is generalized in two directions: in the bivariate case and for arbitrary dimensions.
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01 Aug 2000
Abstract: In the present paper, C1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonie interpolant to a given monotonie data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a C2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.
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TL;DR: Through the investigation of a lot of examples, a `reasonable good' fitting curve to the data is found and it is found that polynomial least squares approximation and exponential spline interpolation are good algorithms for interpolation and approximation to data.
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TL;DR: In this article, the authors studied the problem of scattered cardinal Hermite interpolation and established a necessary and sufficient condition for the solvability of the interpolation scheme, which is similar to the condition in this paper.
Abstract: We study the problem of scattered cardinal Hermite interpolation and establish a necessary and sufficient condition for the solvability of the interpolation scheme.