导　　师： 李松

学科专业： 070104

授予学位： 硕士

作　　者： ;

机构地区： 浙江大学

摘　　要： 本文研究如下形式的正交、插值尺度向量构造算法其中尺度向量Φ=/(φ/_0，…，φ/_/(m-1/)/)~T∈/(L~1/(R~d/)/)~r，{ρ/_i}是Z~d／MZ~d的完备代表集合，M是元素为整数的d×d的矩阵。本文在介绍了正交、插值尺度向量构造算法之后，又研究了该类算法构造出来的正交、插值尺度向量缺乏对称性，更进一步地得到了对称的正交插值尺度向量的必要条件；还得到了如下结果：设Φ=/(φ/_0，…，φ/_/(R-1/)/)~T是细分方程/(1．1/)的连续的规范化解，且面具满足/(2．1/)式，则有是插值的充要条件是Cascade算法收敛。 In this paper we investigate the orthogonal interpolating scaling vectors, which has the formwhere the scaling vectorsΦ= /(φ/_0,…,φ/_/(m-1/)/)~T belongs to /(L~1/(R~d/)/)~r, {ρ/_i} is the completeset of representatives of Z~d//MZ~d ,and M is d×d integer matrix. After introducingthe algorithm for construction of interpolating scaling vectors, we obtain that this kind of orthogonal interpolating scaling vectors constructed by the algorithm can not be symmetric, moreover, we obtain the necessary conditions for constructing symmetric orthogonal interpolating scaling vectors. we also obtain: letΦ= /(φ/_0,…,φ/_/(r-1/)/)~T be the normalized solution of refinement equation/(1.1/), and if the mask of /(1.1/) satisfies /(2.1/), thenΦis interpolating if and only if the Cascade algorithm converges.

关 键 词： 插值 正交 面具 尺度向量 对称

分 类 号： [TP391.41]

领　　域： [自动化与计算机技术] [自动化与计算机技术]