Construction of multiwavelets with high approximation order and symmetry

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 Φ^new(x):= (φ₁^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 Φ^new(x). To embody our results, we construct a symmetric refinable function vector with approximation order 6 from Hermite cubics which provides approximation order 4. This work was supported by the Natural Science Foundation of Guangdong Province (Grant Nos. 05008289, 032038) and the Doctoral Foundation of Guangdong Province (Grant No. 04300917)