节点文献
(L_p(R~s))~r(1≤p≤∞)中细分格式的收敛阶
Convergence rates of cascade algorithms in(L_p(R~s))~r(1≤p≤∞)spaces.
【摘要】 研究细分方程φ(x)=∑α∈Zsa(α)φ(Mx-α),x∈Rs,其中向量值函数φ=(φ1,φ2,…,φr)T∈(Lp(Rs))r(1≤p≤∞),a(α)是具有有限长的r×r矩阵值序列,称为面具,M是一个s×s整数矩阵且满足li mn→∞M-n=0.定义φn∶=Qanφ0,n=1,2,…,其中,Qaφ(x)=∑α∈Zsa(α)φ(Mx-α),φ∈(Lp(Rs))r,函数列{φn}n≥0称为细分格式或级联序列.利用由M,a(α)以及集合E生成的有限线性算子的联合谱半径来刻画与a,φ0,M有关的细分格式{φn}n≥0的收敛阶,其中集合E表示含0的商群Zs/MZs的不同代表元.
【Abstract】 A refinement equation of the form φ(x)=∑α∈Zsa(α)φ(Mx-α),x∈Rs is concerned,where the vector og functions φ=(φ1,φ2,…,φr)T∈(Lp(Rs))r(1≤p≤∞) is unknown,a is a finitely supported sequence of r×r matrices called refinement mask,and M is an s×s integer matrix so that(lim)n→∞M-n=0.The cascade algorithms is associated with a,M generates a sequence φn=Qanφ0,n=1,2,… by Qaφ(x)=∑α∈Zsa(α)φ(Mxα),φ∈(Lp(Rs))r,from a starting vector of function φ0 in(Lp(Rs))r(1≤p≤∞).The aim is to give a characterization of convergence rates of the cascade algorithms {φn} in terms of the p-norm joint spectral radius of a finite collection of some linear operators determined by a and the set E,where the set E is a complete set of representatives of the distinct cosets of the quotient group Zs/MZs containing 0.
【Key words】 refinement equations; joint spectral radius; (L_p(R~s))~r(1≤p≤∞) spaces; cascade algorithms; convergence rates;
- 【文献出处】 浙江大学学报(理学版) ,Journal of Zhejiang University(Science Edition) , 编辑部邮箱 ,2006年03期
- 【分类号】O174.41
- 【下载频次】23