逐次有理L_2逼近的收敛性

设Rn(x)∈Rlm={P(x)/Q(x)},(n=1,2,…)是函数f(x)的第n次最佳L2逼近元,记Sn(x)=∑nk=1Rk(x),(n=1,2,…),在某些附加条件下证明了序列{Sn(x)}一致收敛于f(x),给出了序列{Sn(x)}一致收敛于f(x)的充要条件,并在另一较弱条件下证明了序列{Rn(x)}及其各阶导函数序列{R(k)n(x)},(k=1,2,…)一致收敛于零。

实函数样条插值的L_2逼近

我们构造一个n次样条s_n~*(x),它是一个在给定的m个不同结点上对已给实函数f∈L_(?)~2进行联合插值,满足s_n^(*^(j))(x_0+0)=f^(j)(x_0+0),s_n^(*^(j))(x_m-0)=f^(j)(x_m-0),s_n^(*^(j))(x_i)=f^(j)(x_i),j=1,2,…,m-1,j=0,1,…,v;在L_2范数下,在f的所有同样性质的插值样条当中,它又是f的最佳逼近,且得到f∈C[a,b],n→∞时,有∥s_n~*-f∥L_2→O。

多重插值条件下的L_2逼近

我们构造一个多项式p_(m.n),它既是对给定的函数f∈L_2[a,b]在给定的几个结点上的υ次插值,又是在同样性质的插值下次数小于等于m的多项式中到f的最佳逼近,并且当f∈C[a,b],m→∞是‖p_(m.n)-f‖L_2→0。

联合插值限制的实值函数的L_2逼近

我们构造一个ｍ次多项式ｐｍ，ｎ，它是一个在给定的几个不同的结点上对已给实函数ｆ∈Ｌ＾２１，∞进行联合插值，满足Ｐｍ，ｎ（ｘｉ）＝ｆ（ｘｉ），Ｐｍ，ｎ’（Ｘｉ），ｉ，…，ｎ，在Ｌ２范数下，在ｆ的所有同样性质的插值多项式中，它又是ｆ的最佳逼近，并且得到当ｆ∈Ｃ「ａ，ｂ」，ｍ→∞，‖Ｐｍ，ｎ－ｆ‖→０。

最佳L_2局部逼近为非空凸集的充分条件

本文给出了最佳L_2局部逼近之集P_0(f)为非空凸集的充分条件:f∈C^(n-2)〔0,δ〕,f^(n-2)(x)在x=0处满足Lipschitz条件。

L_2逼近高精度格式的基本原理及其应用

In the present paper, a new numerical method: L2 approximation high accurate scheme is developed. The solution obtained by using this method satisfies not only at the discrete points, but also approximates to the exact solution in the total region. The basic principle is introduced and this method is used to solve some problems. The results show its high accuracy, high resolution and other advantages.

A class of nonconforming quadrilateral finite elements for incompressible flow

This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow.Beyond the previous research works,we propose a general strategy to construct the basis functions.Under several specific constraints,the optimal error estimates are obtained,i.e.,the first order accuracy of the velocities in H1-norm and the pressure in L2-norm,as well as the second order accuracy of the velocities in L2-norm.Besides,we clarify the differences between rectangular and quadrilateral finite element approximation.In addition,we give several examples to verify the validity of our error estimates.