Raising approximation order of refinable vector by increasing multiplicity  

作　　者：YANG Shouzhi & PENG Lizhong Department of Mathematics, Shantou University, Shantou 515063, China LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China 

出　　处：《Science China Mathematics》2006年第1期86-97,共12页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.90104004&10471002);973 project of China(Grant No.G1999075105);the Natural Science Foundation of Guangdong Province(Grant No.05008289&032038);the Doctoral Foundation of Guangdong Province(Grant No.04300917).

摘　　要：An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a. Let φ(x) = [φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function φnew(x) = [ φT(x). f3r+1(x),φr+2(x),…,φr+s(x)}T with the approximation order m + L(L ∈ Z+). In other words, we raise the approximation order of multiscaling function φ(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function φ(x) = [φ1 (x), φ2(x), …, φr(x)]T is symmetric, then the new orthogonal multiscaling function φnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given.An algorithm is presented for raising an approximation order of any given or thogonal multiscaling function with the dilation factor a. Let Ф(x) = [φ1(x), φ2 (x), … , φr (x)]Tbe an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function Фnew(x) = [ ФT(x),φr+1(x), φr+2(x),… ,φr+s(x)]T with the approximation order m + L(L ∈ Z+). In other words, we raise the approximation order of multiscaling function Ф(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function Ф(x) = [φ1(x), φ2(x), … , φr (x)]T is symmetric, then the new orthogo nal multiscaling function Фnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given.

关 键 词：orthogonal  MULTISCALING functions  approximation order  symmetry. 

分 类 号：O174.2[理学—数学]