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Cardinal Hermite Spline Interpolation with Shifted Nodes

1994
*
Mathematics of Computation
*

*Generalized*cardinal

*Hermite*

*spline*

*interpolation*is considered. A special case of this problem is the classical cardinal

*Hermite*

*spline*

*interpolation*with shifted nodes. ... This algorithm is shown to be also applicable to computing the periodic

*Hermite*

*spline*

*interpolant*. ... For solving the

*generalized*

*Hermite*

*spline*

*interpolation*problem for r > 2, the Euler-Frobenius functions hrm " (u = 0, ... , r -1) can be similarly introduced by using

*B*-

*splines*with r-fold knots. 3. ...

##
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Geodesic Hermite Spline Curve on Triangular Meshes

2021
*
Symmetry
*

The conventional

doi:10.3390/sym13101936
fatcat:s67gft3g6jg6djbbi6leecgjcm
*Hermite**interpolation*method is extended such that the*generated*curve lies on M. ... By combining cubic*Hermite**interpolation*and newly devised geodesic operations, a geodesic*Hermite**spline*curve is constructed on a triangular mesh. ... Finally, the geodesic*Hermite**spline*curve consists of a set of cubic Bézier curves*generated*by this method.*Hermite**Spline*Curve The method is based on*Hermite**interpolation*. ...##
###
Cardinal Hermite spline interpolation with shifted nodes

1994
*
Mathematics of Computation
*

*Generalized*cardinal

*Hermite*

*spline*

*interpolation*is considered. A special case of this problem is the classical cardinal

*Hermite*

*spline*

*interpolation*with shifted nodes. ... This algorithm is shown to be also applicable to computing the periodic

*Hermite*

*spline*

*interpolant*. ... For solving the

*generalized*

*Hermite*

*spline*

*interpolation*problem for r > 2, the Euler-Frobenius functions hrm " (u = 0, ... , r -1) can be similarly introduced by using

*B*-

*splines*with r-fold knots. ...

##
###
Real-time interpolation of streaming data

2020
*
Computer Science
*

The results presented show that the cubic

doi:10.7494/csci.2020.21.4.3932
fatcat:vcixlw2obbaknn6tmmluhrqhdq
*Hermite**splines**generated*by heuristic MinAJ2 significantly outperformed these based on finite difference schemas in terms of all tested performance measures ( ... One of the key elements of real-time $C^1$-continuous cubic*spline**interpolation*of streaming data is an estimator of the first derivative of the*interpolated*function that is more accurate than the ones ... The proposed approach is quite*general*. It can be directly applied to streams of univariate functional data like time-series. ...##
###
Efficient Algorithms for Periodic Hermite Spline Interpolation

1992
*
Mathematics of Computation
*

Periodic

doi:10.2307/2153209
fatcat:o5ogpkybsrbudlctgzqvpdoyta
*Hermite**spline**interpolants*on an equidistant lattice are represented by the Bézier technique as well as by the fi-*spline*method. ... Applying the known de Casteljau algorithm and the de Boor algorithm, respectively, we obtain new efficient real algorithms for periodic*Hermite**spline**interpolation*. (cf. [2]). ... Further, one can see that the*generalized*Euler-Frobenius polynomials are very important for periodic*Hermite**spline**interpolation*. ...##
###
Efficient algorithms for periodic Hermite spline interpolation

1992
*
Mathematics of Computation
*

Periodic

doi:10.1090/s0025-5718-1992-1122075-0
fatcat:omlw2upwvrgttcl7buh3nvlaou
*Hermite**spline**interpolants*on an equidistant lattice are represented by the Bézier technique as well as by the fi-*spline*method. ... Applying the known de Casteljau algorithm and the de Boor algorithm, respectively, we obtain new efficient real algorithms for periodic*Hermite**spline**interpolation*. (cf. [2]). ... Further, one can see that the*generalized*Euler-Frobenius polynomials are very important for periodic*Hermite**spline**interpolation*. ...##
###
Adjustable Piecewise Quartic Hermite Spline Curve with Parameters

2021
*
Mathematical Problems in Engineering
*

the classical cubic

doi:10.1155/2021/2264871
fatcat:77aoxtfyavdzzkiypamhgeurli
*Hermite**interpolating**spline*curves. ... In this paper, the quartic*Hermite*parametric*interpolating**spline*curves are formed with the quartic*Hermite*basis functions with parameters, the parameter selections of the*spline*curves are investigated ... Basic Concepts of Cubic*Hermite**Interpolation**Spline*Definition 1. ...##
###
Statistical optimality of Hermite splines

2015
*
2015 International Conference on Sampling Theory and Applications (SampTA)
*

*Hermite*

*splines*are commonly used for

*interpolating*data when samples of the derivative are available, in a scheme called

*Hermite*

*interpolation*. ... We focus on second-order Lévy processes-the integrated version of Lévy processes-and rely on cubic

*Hermite*

*splines*to approximate the original continuous-time signal from its samples and its derivatives ... (e) Reconstruction s Her of the original continuous-time process s using

*Hermite*

*spline*

*interpolation*. ...

##
###
Developments in bivariate spline interpolation

2000
*
Journal of Computational and Applied Mathematics
*

The aim of this survey is to describe developments in the ÿeld of

doi:10.1016/s0377-0427(00)00346-0
fatcat:42yhs4ss7zapzng54jhwewst6m
*interpolation*by bivariate*splines*. ... We summarize results on the dimension and the approximation order of bivariate*spline*spaces, and describe*interpolation*methods for these spaces. Moreover, numerical examples are given. ...*Generally*, given a basis {*B*i ; i = 1; : : : ; d}, of a*spline*space and a set of linear functionals { i : i = 1; : : : ; d}, a quasi-*interpolant*s f of a su ciently smooth function f from this*spline*...##
###
About one method of constructing Hermite trigonometric splines
[article]

2021
*
arXiv
*
pre-print

The method of constructing trigonometric

arXiv:2110.04779v1
fatcat:tepxzrb75rbbxnzc6ftrqlfvk4
*Hermite**splines*, which*interpolate*the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. ... Examples of construction of trigonometric*Hermite**splines*of the first and second orders are given. The proposed method can be recommended for practical use. ... Note that the problem of constructing a*Hermite*polynomial polynomial on a segment in*general*is considered in detail, for example, in [2] ; the construction of*Hermite*polynomial*splines*is considered ...##
###
On Convexity Preserving C1 Hermite Spline Interpolation

1995
*
Computer Science Journal of Moldova
*

The problem of convexity preserving

doaj:876618499e2445d2a68cc755c18c8d7d
fatcat:yqndh36zh5bzxmfhbpkftjncs4
*interpolation*using C1*Hermite**splines*with one free*generating*function is considered. ... The aim of this paper is to present a*general*approach to the problem of shape preserving*interpolation*. ... For the parabolic*Hermite**splines**generated*by the function (4) we get that these*splines*preserve convexity(concavity) of data if the additional knot τ on the mesh is choosen so, that τ > 1 − 2λ i for ...##
###
Page 8485 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

The authors discuss

*generalized**B*-*splines*(GB-*splines*). ... Interconnections between*generalized**B*-*splines*and*B*-*splines*are established. Special attention is paid to the case of the uniformly spaced knots.” 99m:41013 41A15 41A29 Ksasov, Boris I. ...##
###
Page 8027 of Mathematical Reviews Vol. , Issue 2001K
[page]

2001
*
Mathematical Reviews
*

This is a survey of recent progress on

*generalized**Hermite*-Fejér*interpolation*, in particular for Chebyshev nodes. ...*Generalized**Hermite*-Fejér*interpolation*is an*interpolation*method which uses polynomials whose derivatives up to a certain order m vanish at the prescribed*interpolation*nodes. ...##
###
Hermite Snakes With Control of Tangents

2016
*
IEEE Transactions on Image Processing
*

Our curve model relies on

doi:10.1109/tip.2016.2551363
pmid:27071167
fatcat:wqw76nheajhp7flz55u4fpkbn4
*Hermite**spline**interpolation*and can easily*generate*curves with sharp discontinuities; it also grants direct access to the tangent at each location. ... With these two features, the*Hermite*snake distinguishes itself from classical*spline*-snake models and allows one to address certain bioimaging problems in a more efficient way. ... Fig. 6 . 6*Generation*of sharp corners using (a) traditional cubic-*spline*snake, (*b*) exponential-*spline*snake, and (c)*Hermite*-*spline*snake. ...##
###
Support and Approximation Properties of Hermite Splines
[article]

2019
*
arXiv
*
pre-print

Then, we precisely quantify the approximation power of

arXiv:1902.02565v2
fatcat:pgujjgiytbhwdaoc5hycimxhhi
*Hermite**splines*for reconstructing functions and their derivatives, and show that they are asymptotically identical to cubic*B*-*splines*for these tasks ...*Hermite**splines*therefore combine optimal localization and excellent approximation power, while retaining*interpolation*properties and closed-form expression, in contrast to existing similar approaches ... ), and*interpolating*, which is not the case for cubic*B*-*splines*. ...
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