Construction of multiwavelets with high approximation order and symmetry  

作　　者：YANG ShouZhi LI YouFa 

机构地区：[1]Department of Mathematics,Shantou University,Shantou 515063,China

出　　处：《Science China Mathematics》2009年第8期1607-1616,共10页中国科学：数学（英文版）

基　　金：supported by the Natural Science Foundation of Guangdong Province (Grant Nos. 05008289,032038);the Doctoral Foundation of Guangdong Province (Grant No. 04300917)

摘　　要：In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x):= (φ1(x), ..., φr(x)) T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x):= (φ 1 new (x), ..., φ r new (x)) T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally, we reveal the relation between Φ(x) and Φnew(x). To embody our results, we construct a symmetric refinable function vector with approximation order 6 from Hermite cubics which provides approximation order 4.In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally, we reveal the relation between Φ(x) and Φnew(x). To embody our results, we construct a symmetric refinable function vector with approximation order 6 from Hermite cubics which provides approximation order 4.

关 键 词：refinable function vectors MULTIWAVELETS approximation order SYMMETRY 42C15 94A12 

分 类 号：O174.41[理学—数学]