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Means and Hermite Interpolation
, 2008
"... Let m2 < m1 be two given nonnegative integers with n = m1+m2+1. For suitably differentiable f, we let P, Q ∈ πn be the Hermite polynomial interpolants to f which satisfy P (j) (a) = f (j) (a), j = 0, 1,..., m1 ..."
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Let m2 < m1 be two given nonnegative integers with n = m1+m2+1. For suitably differentiable f, we let P, Q ∈ πn be the Hermite polynomial interpolants to f which satisfy P (j) (a) = f (j) (a), j = 0, 1,..., m1
On the Hermite interpolation polynomial
"... Abstract. The Newton form for the Hermite interpolation polynomial using the divided differences with multiple knots is proved. Using this representation, sufficient conditions for the convergence of the sequence of Hermite interpolation polynomials are established. One extends this way a result obt ..."
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Abstract. The Newton form for the Hermite interpolation polynomial using the divided differences with multiple knots is proved. Using this representation, sufficient conditions for the convergence of the sequence of Hermite interpolation polynomials are established. One extends this way a result
HERMITE AND HERMITE–FEJÉR INTERPOLATION FOR STIELTJES POLYNOMIALS
"... Abstract. Let wλ(x):=(1−x2) λ−1/2 and P (λ) n be the ultraspherical polynomials with respect to wλ(x). Then we denote by E (λ) n+1 the Stieltjes polynomials with respect to wλ(x) satisfying � 1 wλ(x)P ..."
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Cited by 2 (2 self)
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Abstract. Let wλ(x):=(1−x2) λ−1/2 and P (λ) n be the ultraspherical polynomials with respect to wλ(x). Then we denote by E (λ) n+1 the Stieltjes polynomials with respect to wλ(x) satisfying � 1 wλ(x)P
Verbs and Adverbs: Multidimensional Motion Interpolation Using Radial Basis Functions
 IEEE Computer Graphics and Applications
, 1998
"... This paper describes methods and data structures used to leverage motion sequences of complex linked figures. We present a technique for interpolating between example motions derived from live motion capture or produced through traditional animation tools. These motions can be characterized by emoti ..."
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Cited by 351 (5 self)
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them, allowing an animated figure to exhibit a substantial repertoire of expressive behaviors. A combination of radial basis functions and low order polynomials is used to create the interpolation space between example motions. Inverse kinematic constraints are used to augment the interpolations
On Multivariate Hermite Interpolation
 ADVANCES COMPUT. MATH
, 1995
"... 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 in ..."
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Cited by 16 (2 self)
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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
Trigonometric wavelets for Hermite interpolation
 Math. Comp
, 1994
"... Abstract. The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0,2π). Two wav ..."
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Cited by 4 (1 self)
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Abstract. The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0,2π). Two
On A Hermite Interpolation By Polynomials Of Two Variables
 SIAM J. Numer. Anal
, 2002
"... 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. It includes Lagrange interpolation as a special case. The uniq ..."
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Cited by 6 (6 self)
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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. It includes Lagrange interpolation as a special case
Hermite Interpolation and Sobolev Orthogonality
, 1999
"... Abstract. In this paper, we study orthogonal polynomials with respect to the bilinear form where (f, g)S = V(f)AV(g) T +〈u, f (N) g (N) 〉, V(f) = (f (c0), f ′ (c0),...,f (n0−1) (c0),...,f(cp), f ′ (cp),...,f (np−1) (cp)), u is a regular linear functional on the linear space P of real polynomials, c ..."
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Abstract. In this paper, we study orthogonal polynomials with respect to the bilinear form where (f, g)S = V(f)AV(g) T +〈u, f (N) g (N) 〉, V(f) = (f (c0), f ′ (c0),...,f (n0−1) (c0),...,f(cp), f ′ (cp),...,f (np−1) (cp)), u is a regular linear functional on the linear space P of real polynomials, c
Barycentric Hermite interpolation
 SIAM J. Sci. Comput
"... Abstract. Let z1,..., zK be distinct grid points. If fk,0 is the prescribed value of a function at the grid point zk, and fk,r the prescribed value of the rth derivative, for 1 ≤ r ≤ nk − 1, the Hermite interpolant is the unique polynomial of degree N − 1 (N = n1 + · · · + nK) which interpolates ..."
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Cited by 2 (0 self)
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Abstract. Let z1,..., zK be distinct grid points. If fk,0 is the prescribed value of a function at the grid point zk, and fk,r the prescribed value of the rth derivative, for 1 ≤ r ≤ nk − 1, the Hermite interpolant is the unique polynomial of degree N − 1 (N = n1 + · · · + nK) which interpolates
HigherOrder HermiteFejér Interpolation for Stieltjes Polynomials
"... Let ( ) := (1− 2 ) −1/2 and , be the ultraspherical polynomials with respect to ( ). Then, we denote the Stieltjes polynomials . In this paper, we consider the higherorder HermiteFejér interpolation operator +1, based on the zeros of , +1 and the higher order extended HermiteFejér interpolation ..."
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Let ( ) := (1− 2 ) −1/2 and , be the ultraspherical polynomials with respect to ( ). Then, we denote the Stieltjes polynomials . In this paper, we consider the higherorder HermiteFejér interpolation operator +1, based on the zeros of , +1 and the higher order extended HermiteFejér interpolation
Results 1  10
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