指定结点重数的最优求积公式

本文通过完全样条和单样条之间的对偶关系,证明了关于函数类W_∞~r的(r_1,…r_n)型最优求积公式存在且唯一。     

ON UNIQUENESS OF SOLUTION TO POINTWISE LANDAU PROBLEM ON THE FINITE INTERVAL

1. Introduction Let W_∞~((r)) (β) = {f| f∈W_∞~((r)) [-1,1], ||f||_(C[-1,1]) β, ||f~((r))||_∞ 1}.In this paper, we will consider the following Landau problem:λf~((k))(ξ) + μf~((k-1)) (ξ) →inf, f∈W_∞~((r)) (β), (1.1)where ξ∈[-1,1], 1(?)k(?)r-1, and λ, μ real and not all zero, (if k=1,suppose λ≠0 in addition ). A. Pinkus studied it first. To begin with, we introduce some fundamental definitions anddenotions. The perfect spline f, which satisfies || f~((r))||_∞ = 1 andhas n knots and n+r+1 points of equioscillation in [-1,1], isdenoted by x_(nr), which is refered as Tchebyshev perfect spline. And     

四边形网格的削角细分

提出了一种四边形网格的削角细分方法(Corner-Cuttmg Subdivision Scheme).每细分一次,四边形网格数目增加为原来的两倍,两次细分结果相当于一次二分对偶细分(Binary Dual Subdivision)和一个旋转.细分算法采用线性细分加平滑的形式,具体地讲平滑是采用两次重复平均的方法,因此其生成曲面具有C1连续性.而且由于这种细分方法对网格几何操作简单,所得网格数据量增长相对缓慢,更适合于3D图像重构及网络传输等应用领域..     

基于L~1度量分析的图象分解与重构算法

Mallat‘s decompositon and reconstruction algorithms are very important in the the field of wavelet theory and its applications to signal processing.Wavelet Anal-ysis,which is based on L^2(R) space,can eliminate redundancy of signals with the help of orthogonality and characterize the processing precision with the meansquare error.In the recent years,it is understood that the mean square measuredoes not match human visual sensitivity well.From the point of view,R.DeVore studied L^1 measure instead.Similarly,considering the principles of image com-pression,Yang introduced and dealt with orthogonality in L^1 space based on thebest approximation theory,and consequently established the corresponding decom-position and reconstruction algorithms for signals.In this paper,error analyses for the algorithms above are taken and the selection of the best parameters in the algorithms are discussed in detail.Finally,the algorithms are compared with the classical Haar and Daubechies‘‘s orthogonal wavelets based on the singal-to-noiseratio data computed.     

SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.     

插值样条的敛散性与边界条件的关系

在[1]中,我们曾经讨论了五次样条插值的最优误差界和边界条件的关系,并指出了,即使结点是等距的,对某些边界条件,插值样条仍可能是发散的.本文讨论更为一般的情况,指出了对任意次多项式样条,当边界条件取某些形式时,插值样条是发散的.     

样条共轭插值与L_p模误差估计

[1—5]讨论了各种类型插值样条的L_∞模最优误差估计。本文利用共轭插值样条,给出一些插值样条类的L_1模最优误差界,然后用插值空间理论导出L_p模估计的上界。 一、样条共轭插值 设n≥1并给定[0,1]上的两个分划:     

HB样条零点个数的上界

§1.引言 设有区间[α,b]上的一个分划 △={α=x_0相似文献   

五次Hermite插值样条的最优误差界

<正> [1]对等距分划下单结点的五次插值样条作出了最优误差估计,本文将给出等距分划下五次Hermite插值样条的最优误差界. 先引入一些记号与定义. 向量(a_1,…,a_n)的弱变号数和强变号数分别记为S~-(a_1,…,a_n)和S~+(a_1,…,a_n).     

关于混合插值样条

本文中我们提出一类特殊的H-B插值问题,即所谓混合插值.我们首先讨论五次样条,它是将Meir和Sharma的缺插值样条中的二阶导数的逐点插值换成一阶导数与二阶导数的交替插值.然后又讨论了三次样条,将[3]中讨论的(p)型插值改成一阶导数及函数值本身在节点处的交替插值.我们研究了这两类样条的存在、唯一性,并得到了它