Abstract
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 new1 (x), ..., φ new r (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.
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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)
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Yang, S., Li, Y. Construction of multiwavelets with high approximation order and symmetry. Sci. China Ser. A-Math. 52, 1607–1616 (2009). https://doi.org/10.1007/s11425-009-0068-9
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DOI: https://doi.org/10.1007/s11425-009-0068-9