THE ELLIPTIC TYPE NODE CONFIGURATION AND INTERPOLATION IN R~2

1.IlltroductionInthispaper,weusetheusualmultivariatenotationac=yi'w'B,iii=if ... j.(if,'',j.EZ )[l'a]andletPnbethe(bivariate)polynomialspaceofallreal(bivariate)polynomialsofdegreeatmostn.NowweintroducetheconceptoftheCurveTypeNodeConfiguration(CTNC):De…     

Progressive stable interpolation

In this paper, we study several interpolating and smoothing methods for data which are known “progressively”. The algorithms proposed are governed by recurrence relations and our principal goal is to study their stability. A recurrence relation will be said stable if the spectral radius of the associated matrix is less than one. The iteration matrices depend on shape parameters which come either from the connection at the knots, or from the nature of the interpolant between two knots. We obtain various stability domains. Moving the parameters inside these domains leads to interesting shape effects. This revised version was published online in June 2006 with corrections to the Cover Date.     

(0,m_1,…,m_q)缺项整插值算子在Besov空间中的逼近

本文研究了在Besov空间中 ,(0 ,m1,… ,mq)整插值算子的逼近和饱和问题 ,确定了逼近的饱和类与饱和阶     

Asymptotic Conditions for Degree Diminution Along Prescribed Lines

One of the problems in bivariate polynomial interpolation is the choice of a space of polynomials suitable for interpolating a given set of data. Depending on the number of data, a usual space is that of polynomials in 2 variables of total degree not greater than k. However, these spaces are not enough to cover many interpolation problems. Here, we are interested in spaces of polynomials of total degree not greater than k whose degree diminishes along some prescribed directions. These spaces arise naturally in some interpolation problems and we describe them in terms of polynomials satisfying some asymptotic interpolation conditions. This provides a general frame to the interpolation problems studied in some of our recent papers.     

A note on Thielen-fractions

In this paper we construct ann-fraction which is a generalization of a Thiele continued fraction. We prove that, under certain conditions, themth approximant of thisn-fraction solves the vector case of the rational interpolation problem.     

Piecewise linear interpolants to Lagrange and Hermite convex scattered data

This paper concerns two fundamental interpolants to convex bivariate scattered data. The first,u, is the supremum over all convex Lagrange interpolants and is piecewise linear on a triangulation. The other,l, is the infimum over all convex Hermite interpolants and is piecewise linear on a tessellation. We discuss the existence, uniqueness, and numerical computation ofu andl and the associated triangulation and tessellation. We also describe how to generate convex Hermite data from convex Lagrange data.Research partially supported by the EU Project FAIRSHAPE, CHRX-CT94-0522. The first author was also partially supported by DGICYT PB93-0310 Research Grant.     

矩形网格上二元切触插值的表现公式

In this paper, we make use of the generalized Vandermonde matrix, and set up formula of bivariate contact interpolation over rectangular grids and a example is given.     

Clarkson and Random Clarkson Inequalities for Lr(X)

We first show how (p,p′) Clarkson inequality for a Banach space X is inherited by Lebesgue-Bochner spaces L_r(X), which extends Clarkson's procedure deriving his inequalities for L_p from their scalar versions. Fairly many previous and new results on Clarkson's inequalities, and also those on Rademacher type and cotype at the same time (by a recent result of the authors), are obtained as immediate consequences. Secondly we show that if the (p, p') Clarkson inequality holds in X, then random Clarkson inequalities hold in L_r(X) for any 1 ≤ r ≤ ∞; the converse is true if r = p'. As corollaries the original Clarkson and random Clarkson inequalities for L_p are both directly derived from the parallelogram law for scalars.     

Quadratic Interpolation on Spheres

Riemannian quadratics are C ¹ curves on Riemannian manifolds, obtained by performing the quadratic recursive deCastlejeau algorithm in a Riemannian setting. They are of interest for interpolation problems in Riemannian manifolds, such as trajectory-planning for rigid body motion. Some interpolation properties of Riemannian quadratics are analysed when the ambient manifold is a sphere or projective space, with the usual Riemannian metrics.     

Hilbert边值问题的逼近解法

讨论了与单位圆上的线性Ｈｉｌｂｅｒｔ边值问题相关的离散Ｈｉｌｂｅｒｔ边值问题，给出了其解法，并且证明了当问题的指标κ＝０时，离散Ｈｉｌｂｅｒｔ边值问题的解强收敛于原Ｈｉｌｂｅｒｔ边值问题的解