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A review of the advance in the theory of wavelet analysis in recent years is given. 相似文献
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[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: 相似文献
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<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). 相似文献
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黄达人 《高校应用数学学报(A辑)》1987,(4)
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。 相似文献
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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 相似文献
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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. 相似文献
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For pre-assigned multiplicities (r_i)_1~n, 1≤r_i≤m, and f∈W_q~m, consider the qu-adrature formulas of type (r_i,…, r_n): 相似文献
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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 相似文献
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本文考虑一般细分方程ψi(x)=Σ1≤j≤NΣk∈Zcij(k)ψj(2x-k),解的存在性,正则性和稳定性,及{ψi}1≤i≤N产生L^p多分辨率分析的条件。 相似文献