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Interpolation - Wikipedia, the free encyclopedia In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points. Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points. For instance, rational interpolation is interpolation by rational functions, and trigonometric interpolation is interpolation by trigonometric polynomials. en.wikipedia.org /wiki/Interpolation   (1045 words)

Hermite interpolation - Wikipedia, the free encyclopedia Hermite interpolation is a method closely related to the Newton divided difference method of interpolation in numerical analysis, that allows us to consider given derivatives at data points, as well as the data points themselves. The interpolation will give a polynomial that has a degree less than or equal to the number of pieces of data given minus 1. This is because the function cannot change more quickly from the estimated Hermite interpolation polynomial than its a-th derivative divided by a! en.wikipedia.org /wiki/Hermite_interpolation   (401 words)

Interpolation methods   (Site not responding. Last check: 2007-10-16) Interpolation as used here is different to "smoothing", the techniques discussed here have the characteristic that the estimated curve passes through all the given points. The parameter mu defines where to estimate the value on the interpolated line, it is 0 at the first point and 1 and the second point. Often a smoother interpolating function is desirable, perhaps the simplest is cosine interpolation. astronomy.swin.edu.au /~pbourke/analysis/interpolation   (618 words)

[No title]   (Site not responding. Last check: 2007-10-16) Hermite cubics C can produce a "visually pleasing" and monotone interpolant to C monotone data. C C Sets derivatives needed to determine a monotone piecewise cubic C Hermite interpolant to the data given in X and F. C Default boundary conditions are provided which are compatible C with monotonicity. May be used by itself C for Hermite interpolation, or as an evaluator for DPCHIM C or DPCHIC. iris.gmu.edu /~snash/nash/software/NMS__double/ch04.f   (7838 words)

Project Hermite   (Site not responding. Last check: 2007-10-16) Because bounding the error in Hermite interpolation in terms of the derivative which kills the interpolating space is of interest in numerical analysis and in the analysis of ordinary differential equations, there is an extensive literature on the subject. Derivative error bounds for Lagrange interpolation: an extension of Cauchy's bound for the error of Lagrange interpolation, G. Howell, J. Approx. Hermite interpolation errors for derivatives, G. Birkhoff and A. Priver, J. Math. www.scitec.auckland.ac.nz /~waldron/Hermite/hermite.html   (507 words)

ipedia.com: Interpolation Article   (Site not responding. Last check: 2007-10-16) The use of the term interpolation in mathematics was inspired in an obvious way by that concept, but is different: it refers to the approximation of a value of a function for which we only know values for a discrete set of values of the independent variable. Interpolation may be used if one does not know the function being interpolated at every point. Interpolation can also be used if we do have a formula, but it takes very long to evaluate. www.ipedia.com /interpolation.html   (959 words)

[No title] This type of interpolation function is called a spline and is formed as follows for the most common case of the cubic spline. Polynomial interpolants for the vector field yield all of the classical polynomial cases along with a rational method for avoiding disasters such as can occur with direct Hermite interpolation with excessively large or discontinuous derivatives. the multi-surface interpolation is equivalent to the cubic Hermite interpolation. www.erc.msstate.edu /publications/gridbook/chap08/text.html   (4804 words)

Citations: Lagrange and Hermite interpolation by bivariate splines - Nurnberger, Riessinger (ResearchIndex)   (Site not responding. Last check: 2007-10-16) Citations: Lagrange and Hermite interpolation by bivariate splines - Nurnberger, Riessinger (ResearchIndex) Results on the approximation order of these interpolation methods were given in [7, 13, 17, 21, 22, 25, 27, 28] In the case of an abitrary triangulation Delta, the finite element method provides a tool to construct Hermite type interpolation schemes for S r q (Delta) with optimal.... Results on the approximation order of these interpolation methods were given in [4, 11, 15, 20, 21, 24, 27, 28] A Hermite interpolation scheme for S 1 q (Delta) q 5, where Delta is an arbitrary triangulation, can be obtained by using a nodal basis of this space constructed in [17] see.... citeseer.ifi.unizh.ch /context/847777/0   (802 words)

MATH2070: LAB 8: Higher Order Interpolation and Mesh Generation   (Site not responding. Last check: 2007-10-16) Hermite interpolation is discussed in Atkinson, Section 3.6. using the expression (3) for the Hermite interpolating polynomial. Hermite cubics will generate smooth mesh lines if the outline of the region is smooth. www.math.pitt.edu /~sussmanm/2070Fall04/lab_08/lab_08.html   (2296 words)

On Multivariate Hermite Interpolation - Sauer, Xu (ResearchIndex) We study the problem of Hermite interpolation by polynomials in several variables. A very general definition of Hermite interpolation is adopted which consists of interpolation of consecutive chains of directional derivatives. We discuss the structure and some aspects of poisedness of the Hermite interpolation problem; using the notion of blockwise structure which we introduced in [10], we establish an interpolation formula analogous to that of Newton in one variable and use it to derive an... citeseer.ist.psu.edu /29014.html   (504 words)

Hermite Curve Interpolation Hermite curves are very easy to calculate but also very powerful. They are used to smoothly interpolate between key-points (like object movement in keyframe animation or camera control). We'll lose some of the flexibility of the hermite curves, but as a tradeoff the curves will be much easier to use. www.cubic.org /docs/hermite.htm   (1073 words)

Vector3.Hermite Method A Vector3 structure that is the result of the Hermite spline interpolation. The spline interpolation is a generalization of the ease-in, ease-out spline. Hermite splines are useful for controlling animation because the curve runs through all of the control points. msdn.microsoft.com /archive/en-us/directx9_m_Summer_04/directx/ref/ns/microsoft.directx/s/vector3/m/hermite.asp?frame=true   (412 words)

Atlas: A Remainder Formula for Hermite Multivariate Interpolation by Dana Simian The aim of this paper is to present and prove a remainder formula in two cases of Hermite interpolation in two variables and to apply this formula to certain particular Hermite interpolation spaces. The two Hermite interpolation cases we study in this article are minimal interpolation spaces with respect to a set of functionals, \Lambda, which more important property is: ker(\Lambda) is a polynomial ideal. (f) the Hermite interpolation operator, and g(D) the differential operator with constant coefficients associated to the bivariate polynomial g. atlas-conferences.com /cgi-bin/abstract/calm-50   (237 words)

Polynomial Interpolation The major focus of the work in polynomial interpolation at the Bendigo campus of La Trobe University has been on the Lagrange and Hermite-Fejér interpolation processes, and on their generalizations. The graphs also suggest that for fixed m, the Lebesgue constant for (0,1,.....,2m) HF interpolation on the Chebyshev nodes is an increasing function of n, the number of nodes. Michael Revers of the University of Salzburg, Austria, is investigating Lagrange interpolation on equally-spaced points. www.latrobe.edu.au /maths/smith/interp.html   (708 words)

[music-dsp] Hermite Interpolation - Question of beginning   (Site not responding. Last check: 2007-10-16) Hermite Interpolation is used when a sampler resamples a sample to play it at a different pitch. Ideally, a sampler should use a combination of lowpass filtering and sinc interpolation, but this is far too slow to be done in realtime. Hermite Interpolation combined with proper lowpass filtering can provide very good results with less aliasing than linear interpolation. shoko.calarts.edu /pipermail/music-dsp/2002-May/015861.html   (175 words)

Vandermonde matrix - Wikipedia, the free encyclopedia are equal, the corresponding polynomial interpolation problem is ill-posed. These matrices are useful in polynomial interpolation, since solving the system of linear equations Vu = y for u with V the n × n Vandermonde matrix is equivalent to finding the coefficients u Confluent Vandermonde matrices are used in Hermite interpolation. en.wikipedia.org /wiki/Vandermonde_matrix   (432 words)

[No title] C Used if the data are monotonic or if the user wants C to guarantee that the interpolant stays within the C limits of the data. C Computes the definite integral of a piecewise cubic C Hermite function when the integration limits are data C points. Fritsch and R. Carlson, Monotone piecewise C cubic interpolation, SIAM Journal on Numerical Ana- C lysis 17, 2 (April 1980), pp. www.netlib.org /slatec/pchip/pchdoc.f   (1061 words)

LAB #8: Piecewise Polynomial Interpolation   (Site not responding. Last check: 2007-10-16) Because you are using quadratic interpolation of a quadratic polynomial, your interpolated results (from paraval) should agree exactly with values from the polynomial you chose. One disadvantage of the Hermite interpolation scheme is that you need to know the derivatives of your function. The continuity and interpolation conditions are almost enough to specify the cubic. www.math.pitt.edu /~troy/math2070/lab_08.html   (2223 words)

Citebase - Conjecture of error boundedness in a new Hermite interpolation problem via splines of odd-degree   (Site not responding. Last check: 2007-10-16) Authors: Balabdaoui, Fadoua; Wellner, Jon A. We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we conjecture that the interpolation error is bounded in the supremum norm independently of the locations of the knots. In this case, the worst interpolation error is proved to be attained by the perfect spline of degree 2k with the same knots as the spline interpolant. citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0509160   (633 words)

SINUM Volume 39 Issue 5 A problem of Hermite interpolation by polynomials of two variables is studied. The interpolation matches preassigned data of function values and consecutive normal derivatives on a set of points on several circles centered at the origin. The uniqueness of the interpolation is established when the points are equidistant on the circles, while the points on different circles may differ by arbitrary rotations. epubs.siam.org /sam-bin/dbq/article/38347   (176 words)

[No title] C***DESCRIPTION C C PCHIP: Piecewise Cubic Hermite Interpolation Package C C This document contains the specifications for PCHIP, a new C Fortran package for piecewise cubic Hermite interpolation of data. As is demonstrated in Reference 1, C such an interpolant may be more reasonable than a cubic spline if C the data contains both "steep" and "flat" sections. C Produces a cubic spline interpolator in cubic Hermite C form. www.umbc.edu /doc/cmlib/doc/pchips/Summary   (935 words)

Abstract   (Site not responding. Last check: 2007-10-16) Hermite routines take as input the function value and derivatives at each grid point, giving back a representation of the function between grid points. The 1D spline and Hermite routines are based on standard methods; the 2D and 3D spline or Hermite interpolation functions are constructed from 1D spline or Hermite interpolation functions in a straightforward manner. Spline and Hermite interpolation functions are often much faster to evaluate than other representations using e.g. w3.pppl.gov /ntcc/PSPLINE/abstract.html   (244 words)

Lecture 20 Hermite_coef - matlab program is a program, which finds the coefficients of a set of data for the Hermite interpolation. Hermite_Eval - matlab program is a program, which uses the coefficients of the Hermite interpolation to find the value at point. Spline1 - matlab program is a program, which uses the Spline technique to interpolate between the given set of data. stommel.tamu.edu /~esandt/Teach/Fall01/CVEN302/Lectures/Lecture20/layout20.html   (391 words)

Polynomial Interpolations To be more precise, assume that we have found a polynomial that interpolates to the n first data points p0,..., pn-1, and also a polynomial that interpolates to the n last data points p1,..., pn. Polynomial interpolation is not restricted to interpolation to point data: one can also interpolate to other information, such as derivative data. The interpolant then becomes where the are defined through their cardinal properties: To satisfy these requirements, the new must differ from the original. www.math.hmc.edu /~gu/math142/mellon/Application_to_CAGD/Interpolations_and_Blossoms/Polynomial_Interpolation.html   (717 words)

Error Estimates and Convergence Rates for Variational Hermite Interpolation - Luo, Levesley (ResearchIndex)   (Site not responding. Last check: 2007-10-16) The optimal Hermite interpolant, which minimises the semi--norm of the reproducing kernel Hilbert space C h determined by given r-CPDm function h, is just the h-spline Hermite interpolant. The results on error estimation and convergence rate of the h-spline interpolant generalise those in [11, 12, 18, 10] to the case of Hermite interpolation. 1 Hermite interpolation on the lattice grid (context) - Jetter, Riemenschneider et al. citeseer.ist.psu.edu /luo97error.html   (520 words)

Publications on Polynomial Interpolation Below is a list of publications (since 1990) in the area of polynomial interpolation by members of the Department of Mathematics and Statistics at the Bendigo campus of La Trobe University. Simon J. Smith, The Lebesgue function for Lagrange interpolation on the augmented Chebyshev nodes, Publ. Simon J. Smith, On the fundamental polynomials for Hermite-Fejér interpolation of Lagrange type on the Chebyshev nodes, J. Inequal. www.latrobe.edu.au /maths/smith/int-publ.html   (524 words)

[No title]   (Site not responding. Last check: 2007-10-16) ; EXPLANATION: ; Hermite interpolation computes the cubic polynomial that agrees with ; the tabulated function and its derivative at the two nearest ; tabulated points. It may be preferable to Lagrangian interpolation ; (QUADTERP) when either (1) the first derivatives are known, or (2) ; one desires continuity of the first derivative of the interpolated ; values. HERMITE() will numerically compute the necessary ; derivatives, if they are not supplied. www.astro.ku.dk /idl_local_lib/astron/pro/hermite.pro   (160 words)

Surface Remeshing by Local Hermite Diffuse Interpolation   (Site not responding. Last check: 2007-10-16) The objective is to determine a local surface equation (second degree) using the nodes of the initial mesh and the normals to the surface calculated from the mesh. The interpolating nodes belong to the set of elements sharing at least one node with the element that includes the point where we calculate the interpolation. The diffuse interpolation leads to the minimization of a criterion which is provided by nodal interpolation and colinearity of normal vectors. www.andrew.cmu.edu /user/sowen/abstracts/Ra628.html   (474 words)

Multivariate polynomial interpolation   (Site not responding. Last check: 2007-10-16) I am interested in bounding the p-norm of the error in a multivariate polynomial interpolation scheme by norms of derivatives which kill the interpolating space (and require the function interpolated to be no smoother than is necessary). The error in linear interpolation at the vertices of a simplex, Waldron 1994). On multivariate polynomial interpolation, C. de Boor and A. Ron, Const. www.scitec.auckland.ac.nz /~waldron/Multivariate/multivariate.html   (864 words)

Documentation for PCHIPD C C DPCHIM -- Piecewise Cubic Hermite Interpolation to Monotone C data. C C DPCHFD -- Piecewise Cubic Hermite Function and Derivative C Evaluator. C C DPCHMC -- Piecewise Cubic Hermite Monotonicity Checker. orion.math.iastate.edu /docs/cmlib/pchipd.html   (935 words)

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