The Approximation Order Of Two-Scaled Similarity And Inverse Two-Scaled Similarity Transforms

After 20 years of development,wavelet analysis becomes a hot field among all scientificresearches, whose application almost concerned with all branches of both natural scienceand engineering technology. Especially, wavelet analysis is considered as an essential tool toresearch and solve many complicated problems in both natural science and engineering com-putation. The article gives the comparatively in-depth discussing and learning of two-scalesimilarity transforms (TST) and the inverse two-scale similarity transforms (ITST),which areapplied in wavelet frame. Through the learning some results are obtained. In the following,the main contents are listed:At first,When the transformation matrix has p values of non-degradation eigenvalue inzero,the definitions of the inverse two-scale similarity transforms (ITST) are obtained.Thenthe changes of approximation order and some theorems in related of the wavelet and multi-wavelet under the definition of ITST are given. We also obtain the forms of approximationvector and the corresponding design examples are given .Second,When the transformation matrix has p values of non-degradation eigenvalue inzero,the definitions of two-scale similarity transforms (TST) are obtained.then ,the changesof approximation order and some theorems in related of the wavelet and multi-wavelet aregiven. We also obtain the forms of approximation vector in the end.