TRUNCATED HERMITE INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

1 IntroductionThis paper deals with the uniform collvergence of truncated Hermte illterpolatioll oll anarbitrary systelll of 11odes. Tl1e mean collvergellce of trllllcated Herntite interpolation oll a11arbitrary syste12l of 1lodes 1las been st11died recently by tlle al1t11or[31. The converge11ce oftruncated Hern1ite illterpolatiou on tl1e zeros of the Jacobi polynontials is discussed in both tlleweigl1ted LP and the unfform norm by P. Vertesi and Y. X.[61.First we iutroduce some defi11itio…     

SOME RESEARCHES ON WEAK CONVERGENCE OF KERGIN INTERPOLATION

The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted （partial） derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang＇s main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.     

UNIFORM CONVERGENCE OF HERMITE INTERPOLATION OF HIGHER ORDER

In this paper the uniform convergence of Hermite-Fejer interpolation and Griinwald type theorem of higher order on an arbitrary system of nodes are presented.     

TRUNCATED HERMITE INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES 1

The criteria of convergence, including a theorem of Grűnwald-type, and the rate of convergence in terms of the modulus ω_φ(f, t) of Ditzian and Totik for truncated Hermite interpolation on an arbitrary system of nodes are given.     

Mean Convergence of Lagrange Type Interpolation on an Arbitrary System of Nodes

Abstract Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in theWeighted L~p norm on an arbitrary system of nodes are given.     

Mean Convergence of Lagrnage Type Interpolation on an Arbitrary System of Nodes

Abstract   Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted L ^p norm on an arbitrary system of nodes are given. Supported by the National Natural Sciences Foundation of China (No.19671082)     

高阶Hermite-Fejér型内插

The paper introduces Hermite-Fejr type (Hermite type) interpolation of higher order denoted by Smn(f)(S*mn(f)), and gives some basic properties including expression formulas, convergence relationship between Smn(f) and Hmn(f) (Hermite-Fejr interpolation of higher order), and the saturation of Smn(f).     

Lagrange插值逼近导数的平均收敛

<正>We consider the rate of mean convergence of derivatives by Lagrange interpolation operators L_n(f,x) based on the zeros of Chebyshev polynomials of the first kind.A sharp estimate of the derivative of L_n(f,x)—f(x) in terms of the error of best approximation by polynomials of degree n is derived.     

对流占优扩散方程的一种特征差分算法

A new kind of characteristic-difference scheme for convection-diffusion equations is constructed by characteristic method and bilinear interpolation method. The convergence of the scheme is proved. The advantages of this scheme are to obtain the solutions of the convection diffusion equations with variable coefficient expediently and to reduce the numerical oscillations of the convectiondominanted diffusion equations effectively.     

A criterion for the uniform convergence of sinc-approximations on a segment

In this paper we obtain a criterion for the uniform convergence inside the interval (0, π) of values of E. T. Whittaker operators

$L_n (f,x) = \sum\limits_{k = 0}^n {\frac{{sin(nx - k\pi )}}{{nx - k\pi }}f\left( {\frac{{k\pi }}{n}} \right)} $

for continuous functions. This criterion is similar to that of A. A. Privalov for the convergence of interpolation Lagrange-Chebyshev polynomials and trigonometric ones.

     

CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS

This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.     

(0,M)插值的推广

本文对周期为2ψ的函数引入了一类新的函数插值并建立了插值的收敛速度估计．通常的Birkhoff插值是该插值的极限情形．     

A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic

Starting from disjoint disks which contain polynomial complex zeros, the new iterative interval method for simultaneous finding of inclusive disks for complex zeros is formulated. The convergence theorem and the conditions for convergence are considered, and the convergence is shown to be fourth. Numerical examples are included.     

Dirichlet级数系数的重排

本文研究了Dirichlet级数系数的重排与此级数的收敛横坐标的关系.利用Knopp-Kojima的方法,获得了在Knopp-Kojima公式下绝对收敛横坐标保持不变的重排特征.     

遗传算法的收敛速度估计

Under some conditions, the convergence of the genetic algorithms is investigated, corresponding convergence rates are estimated, and some related verifications are given in this paper.     

特殊半鞅的收敛集

本文讨论特殊半鞅的收敛集，利用随机过程的控制关系和停时技巧，给出了特殊半鞅的收敛集的一般定理，推广和改进了已有的部分结果．     

在πn(x)零点上的(O，1，3)插值

本文讨论了n为奇数时π_n(x)＝(1-x²)P′_n-1(x)零点上的(0,1,3)插值的正则性及收敛性,其中P_n-1表示n-1次Legendre多项式.     

Convergence of spline collocation for Volterra integral equations

Estimates for step-by-step interpolation projections are established. Depending on the spectrum of the transfer matrix these estimates allow to obtain the pointwise convergence of the projectors to the identity operator or, in some limit cases, to prove stable convergence of the corresponding approximate operators of integral equations. This, via general convergence theorems for operator equations, permits to get the convergence of collocation method for Volterra integral equations of the second kind in spaces of continuous or certain times continuously differentiable functions. Applications in the case of the most practical types of splines are analyzed.     

ON LAGRANGE INTERPOLATION TO ｜x｜^α（1 〈α 〈 2） WITH EQUALLY SPACED NODES

S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [−1,1], In 2000, M. Rever generalized S.M. Lozinskii’s result to |x|^α(0≤α≤1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|^α(1<α<2).