Hermite四点插指公式

文章利用Hermite插值基函数,将求解Hermite四点插指问题转换为求解8个派生出来的多项式插值问题,证明了Hermite四点插指公式的存在唯一性,并用两种方法构造出Hermite四点插指公式,最后给出了一个算例.     

Approximation of finite-section equations by piecewise constant functions

The problem is studied of reducing the amount of discrete information required for achieving a prescribed accuracy of solving Fredholm integral equations of the first kind on a half-line. The equations are solved by the finite-section method combined with piecewise constant interpolation of the kernel and the right-hand side at uniform grid points. The approximating properties of the discretization schemes are examined, and the corresponding computational costs are analyzed.     

Classification of sets satisfying the geometric characterization

The geometric characterization identifies the sets of nodes such that the Lagrange polynomials are products of factors of first degree. We offer a detailed classification of all known sets satisfying the geometric characterization in the plane. The defect, which takes into account the number of lines containing more nodes than the degree, plays a fundamental role in this classification. Partially supported by the Spanish Research Grant MTM2006-03388, by Gobierno de Aragón and Fondo Social Europeo.     

有理插值问题不适定的根本原因

1　在 Rm,n中的有理插值问题本文记 Pn为次数不超过 n的一元多项式函数类 ,约定零多项式的次数为 -∞ ,即deg(0 ) =-∞ ;记 Rm,n为分子属于 Pm,分母属于 Pn\{ 0 }的一元有理函数类 .对既约分式Am/Bn∈Rm,n,如果 Bn满足尾项规范条件 (即 Wuytack条件 ) [2 ] ,则称其为标准既约分式 .引进一个新的有理函数类 ,记Rl =Rl- 1 ,0 ∪ Rl- 2 ,1 ∪…∪ R0 ,l- 1 .称 Rl 是自由度为 l的一元有理函数类 .并称其中有理函数类 Rl- 1 - i,i为有理函数类 Rl 的基本子类 ,(i=0 ,1 ,… ,l-1 ) .我们约定 :本文中“有理插值问题”如不特殊声明 ,系指文…     

Abstract Hardy-Sobolev spaces and interpolation

The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities.     

A Newton type rational interpolation formula

We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the interpolation formula of Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula.     

Stationary Probability Distribution of Colored-noise Saturation Model for a Single-mode Dye Laser

It is applied the interpolation procedure to calculate the stationary probability distribution of colored-gain-noise model of a single-mode dye laser which operates above threshold with correlation time τ covering a very wide rang. By use of Stochastic Runge-Kutta Algorithm, it also has carried out numerical simulations of the steady-state properties. Comparing the results of the interpolation procedure and the unified colored-noise approximation with simulation results, the agreement between the results of the interpolation procedure and simulation results is much better than that of the unified colored-noise approximation when correlation time τ covers range from moderate to large.     

Asymptotically exhaustive functions in Vitali spaces

We introduce asymptotically exhaustive functions defined on Vitali Spaces with values in a Hausdorff commutative topological group and we prove for them some classical convergence theorems. This article was supported by MURST, project “Analisi Reale”     

Monotone and Convex C 1 Hermite Interpolants Generated by a Subdivision Scheme

   Abstract. We propose C ¹ Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates in the case of interpolation of smooth functions.     

Generalized Strang–Fix condition for scattered data quasi-interpolation

Quasi-interpolation is very useful in the study of the approximation theory and its applications, since the method can yield solutions directly and does not require solving any linear system of equations. However, quasi-interpolation is usually discussed only for gridded data in the literature. In this paper we shall introduce a generalized Strang–Fix condition, which is related to nonstationary quasi-interpolation. Based on the discussion of the generalized Strang–Fix condition we shall generalize our quasi-interpolation scheme for multivariate scattered data, too. AMS subject classification 41A63, 41A25, 65D10Zong Min Wu: Supported by NSFC No. 19971017 and NOYG No. 10125102.