• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.963-980
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• 2009

In this paper, spectral scheme based on Hermite interpolation for solving partial differential equations is presented. The idea of this Hermite spectral method comes from the spectral method on arbitrary grids of Carpenter and Gottlieb [J. Comput. Phys. 129(1996) 74-86] using the Lagrange interpolation.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.131-141
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• 2010

In this paper, we propose a new method to obtain $C^1$ MPH quartic Hermite interpolants generically for any $C^1$ Hermite data, by using the speed raparametrization method introduced in [16]. We show that, by this method, without extraordinary processes ($C^{\frac{1}{2}}$ Hermite interpolation introduced in [13]) for non-admissible cases, we are always able to find $C^1$ Hermite interpolants for any $C^1$ Hermite data generically, whether it is admissible or not.

• East Asian mathematical journal
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• v.28 no.1
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• pp.13-23
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• 2012

In this paper, we present the geometric Hermite interpolation for planar Pythagorean-hodograph cubics for some general Hermite data.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.731-740
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• 2002

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

• East Asian mathematical journal
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• v.29 no.1
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• pp.53-68
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• 2013

We solve the geometric Hermite interpolation problem with planar Pythagorean-hodograph cubics. For every Hermite data, we determine the exact number of the geometric Hermite interpolants and represent the interpolants explicitly. We also present a simple criterion for determining whether the interpolants have a loop or not.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.445-456
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• 2008

We characterize the helical polynomial space curves and solve the first-order Hermite interpolation problem for helical polynomial space quintics.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.177-196
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• 2008

Using the results on the coefficients of Hermite-Fej$\acute{e}$r interpolations in [5], we investigate convergence of Hermite and Hermite-$Fej{\acute{e}}r$ interpolation of order m, m=1,2,... in $L_p(0<p<{\infty})$ and associated product quadrature rules for a class of fast decaying even $Erd{\H{o}}s$ weights on the real line.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.43-51
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• 2022

The aim of this paper is to obtain a Radau type quadrature formula for a rational interpolation process satisfying the almost quasi Hermite Fejér interpolatory conditions on the zeros of Chebyshev Markov sine fraction on [-1, 1).

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.73-86
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• 2007

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatial $C^1$ Hermite data, we construct a spatial PH curve on a sphere that is a $C^1$ Hermite interpolant of the given data as follows: First, we solve $C^1$ Hermite interpolation problem for the stereographically projected planar data of the given data in $\mathbb{R}^3$ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in $\mathbb{R}^3$ using the inverse general stereographic projection.