α尺度紧支撑正交多小波的构造

1.引 言 自从Geronimo,Hardin和Massopust[1]使用分形插值函数构造出 GHM-多小波以来,对多小波的研究己引起很多人的关注（see[2]～[5]）.出于多通道滤波理论的需要及欲获得比2尺度小波有更大灵活性的小波,a尺度多小波理论被引入.我们知道,2尺度单一小波己相当成熟,特别是在小波的构造方面,己由I.Daubechies[6]得到非常完美的公式:     

矩阵的正交扩充与多正交小波

给出一种由a尺度紧支撑正交多尺度函数构造短支撑正交多小波的方法,其过程仅仅应用矩阵的正交扩充和求解方程组。如果r重尺度函数的支撑区间较大,可以将其转化为ar重短支撑情形,从而使得本文的方法适用于任意紧支撑正交多小波的构造,文后给出多小波的构造算例。     

多重a尺度双向双正交向量值小波的构造

基于双向向量值小波的基本理论,通过酉矩阵,给出了a尺度r重双向向量值小波双正交条件,得到了a尺度r重双向向量值构造算法,最后给出算例.     

二元紧支撑正交小波的构造

§ 1.　Introduction　　SinceDAUBECHIES [1 ]gavethewellknownconstructionofunivariatecompactlysup portedorthonormalwavelets,considerableattertionhasbeenspentonconstructingmultivariatecompactlysupportedorthonormalwavelets [2— 5etc.] .Althoughmanyspecialbivariatenon separablewaveletshavebeenconstructed ,itisstillanopenproblemhowtoconstructbivariatecompactlyorthonormalwaveletsforanygivencompactlysupportedscalingfunction .Thepur poseofthispaperistoconstructcompactlysupportedorthogonalwaveletass…     

M带紧支撑正交对称复尺度函数的构造

1 引言 近年来,小波的研究主要集中于实值小波,并得到了许多优美的结果。如Daubechies构造一系列2带正交小波,Chui和Lian构造若干3带既正交又对称的尺度函数和小波,杨守志,程正兴等,构造出既正交又对称的4带尺度函数和小波,对M≥3这样的一般情形,Bi,Dai和Sun给出M带正交的Daubechies类尺度函数的通用滤波器表     

a尺度正交多尺度函数和正交多小波

基于a 尺度正交单尺度函数，分别给出重数为2和3的a 尺度正交多尺度函数的构造算法。并给出对应正交多小波的显式构造。最后给出伸缩因子为3的正交多小波的构造算例。     

a尺度多重正交小波包

本文给出了ａ尺度多重正交小波包的构造方法,它是通过对ａ尺度多重正交小波向量等长截取为ａ－１个子向量之后得到的,对同一多重正交小波而言,采用本方法可以构造多种不同的正交小波包,从而使多重正交小波包不仅具有传统的小波包的特点,而且在应用中具有较强的灵活性。     

紧支撑正交插值的多小波和多尺度函数

本文给出一类伸缩因子为α的紧支撑正交插值多尺度函数和多小波的构造方法.设{Vj}是尺度函数Φ(x)=[φ1(x),φ2(x),…,φa(x)]T生成的多分辨分析,Vj(?)L2(R)是{a-j/2φ(?)(ajx-k),k∈Z,(?)=1,2,…,a)线性扩张构成的子空间,其插值性是指φ1(x),φ2(x),…,φa(x)满足φj(k+(?)/a)=δk,0δj,e,j,(?)∈{1,2,…,a).当Φ(x)是正交插值的,则多分辨分析的分解或重构系数能用采样点表示而不需要用计算内积的方法产生.基于此,我们建立多小波采样定理,即如果一个连续信号f(x)∈VN,则f(x)=∑i=0a-1∑k∈Zf(k/aN+i/aN+1)φi+1(aNx-k),并给出对应多小波的显式构造公式.更进一步,证明了本文构造的多小波也有插值性.最后,还给出一个构造算例.     

具有矩阵伸缩的尺度函数双正交特征

考虑了高维具有矩阵伸缩的尺度函数双正交性问题.给出了这种情形下尺度函数双正交性的三个特征刻划及尺度函数属于L2(Rd)的几个充分条件.     

Meyer型正交小波基的构造与性质

本文基于多分辨分析理论与A．W．W方法将Meyer正交小波的构造规范化,给出其设计方法,并证明此类Meyer型小波母函数ψ（x)及相应的尺度函数ψ(x)具有优良的性质,如速降性O（│x│^-N-1(│x│→∞）、N阶消失矩、线性相位、对称性、频谱有限性、并且双尺度序列（滤波器）hn=ψ（n/2）等,并给出N＝2时构造小波函的具体实例。     

a尺度正交的多小波

给出一种构造 a尺度正交多小波的方法 .它是由任意 a尺度正交的单小波及一组滤波器构造出来的 .由于 a尺度单正交尺度函数选取的任意性和滤波器的选取有相当大的自由度 ,使得有可能构造出大量 a尺度正交的多小波 .     

具有矩阵伸缩的双正交小波基

在这篇文章里,我们研究了伸缩为矩阵的双正交小波基的构造问题,在适当条件下,我们得到了Ｌ~２（Ｒ~ｎ）的小波框架或双正交小波基｛ｓｊ,ｋ｝和｛ｓｊ,ｋ｝,其中ｓｊｋ（ｘ）＝ｄｅｔＡｓ（Ａｊｘ－ｋ）,ｓｊ,ｋ（ｘ）＝ｄｅｔＡｊ２ｓ（Ａｊｘ－ｋ）（ｊ Ｚ． ｋ Ｚ~ｎ）及 Ａ是一伸缩矩阵．     

高维多重双正交小波包

本文给出对应于高维多重尺度函数的双正交多小波包的定义及其构造方法.讨论了高维不可分双正交多小波包的双正交性.     

伸缩因子为s的尺度函数傅里叶变换的支集

主要构造出了一类sd-集但非Wsd-集．同时,我们使用一种新方法,推广了一些已知的结果．基于这些结果,系统地揭示了sd-尺度函数的傅里叶变换的支集与闭球的关系．     

Staggered discontinuous Galerkin methods for the incompressible Navier–Stokes equations: Spectral analysis and computational results

The goal of this paper is to create a fruitful bridge between the numerical methods for approximating PDEs in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear systems. Among the main objectives are the design of new, efficient iterative solvers and a rigorous analysis of their convergence speed. The link we have in mind is either the structure or the hidden structure that the involved coefficient matrices inherit, both from the continuous PDE and from the approximation scheme; in turn, the resulting structure is used for deducing spectral information, crucial for the conditioning and convergence analysis and for the design of more efficient solvers. As a specific problem, we consider the incompressible Navier–Stokes equations; as a numerical technique, we consider a novel family of high‐order, accurate discontinuous Galerkin methods on staggered meshes, and as tools, we use the theory of Toeplitz matrices generated by a function (in the most general block, the multilevel form) and the more recent theory of generalized locally Toeplitz matrix sequences. We arrive at a somehow complete picture of the spectral features of the underlying matrices, and this information is employed for giving a forecast of the convergence history of the conjugate gradient method, together with a discussion on new and more advanced techniques (involving preconditioning, multigrid, multi‐iterative solvers). Several numerical tests are provided and critically illustrated in order to show the validity and the potential of our analysis.     

A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients

This paper presents a shifted fractional‐order Jacobi orthogonal function (SFJF) based on the definition of the classical Jacobi polynomial. A new fractional integral operational matrix of the SFJF is presented and derived. We propose the spectral Tau method, in conjunction with the operational matrices of the Riemann–Liouville fractional integral for SFJF and derivative for Jacobi polynomial, to solve a class of time‐fractional partial differential equations with variable coefficients. In this algorithm, the approximate solution is expanded by means of both SFJFs for temporal discretization and Jacobi polynomials for spatial discretization. The proposed tau scheme, both in temporal and spatial discretizations, successfully reduced such problem into a system of algebraic equations, which is far easier to be solved. Numerical results are provided to demonstrate the high accuracy and superiority of the proposed algorithm over existing ones. Copyright © 2015 John Wiley & Sons, Ltd.