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Means and Hermite Interpolation

by Alan Horwitz , 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

by Ovidiu T. Pop
"... 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

by H. S. Jung
"... 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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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

by Charles Rose, Bobby Bodenheimer, Michael F. Cohen - 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 ..."
Abstract - Cited by 351 (5 self) - Add to MetaCart
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

by Thomas Sauer, Yuan Xu - 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 ..."
Abstract - Cited by 16 (2 self) - Add to MetaCart
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

by Ewald Quak - 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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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

by Borislav Bojanov, Yuan Xu - 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 ..."
Abstract - Cited by 6 (6 self) - Add to MetaCart
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

by Esther M. García-caballero, Teresa E. Pérez, Miguel A. Piñar, I Física, Teórica Computacional , 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

by Burhan Sadiq, Divakar Viswanath - 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 r-th derivative, for 1 ≤ r ≤ nk − 1, the Hermite interpolant is the unique polynomial of degree N − 1 (N = n1 + · · · + nK) which interpolates ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
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 r-th derivative, for 1 ≤ r ≤ nk − 1, the Hermite interpolant is the unique polynomial of degree N − 1 (N = n1 + · · · + nK) which interpolates

Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials

by Hee Sun Jung , Ryozi Sakai
"... 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 higher-order Hermite-Fejér interpolation operator +1, based on the zeros of , +1 and the higher order extended Hermite-Fejér 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 higher-order Hermite-Fejér interpolation operator +1, based on the zeros of , +1 and the higher order extended Hermite-Fejér interpolation
Results 1 - 10 of 3,182