QUASI WAVELETS AND QUASI INTERPOLATING WAVELETS

This Letter introduces two families of new wavelets, quasi wavelets an d quasi interpolating wavelets. It is found that the mathematical regu larization of Shannon's orthonormal interpolating wavelet leads to an interplay between a quasi wavelet and a quasi interpolating wavelet. T he resulting quasi wavelet scaling function preserves the interpolatio n property but it does not satisfy the wavelet normalization requireme nt. Whereas the quasi interpolating wavelet scaling function satisfies the normalization requirement but it is no longer rigorously interpol ative. Both quasi wavelets and quasi interpolating wavelets are functi ons of the Schwartz class. Their numerical performance is extremely si milar to each other for data interpolation, differentiation and for so lving partial differential equations. (C) 1998 Elsevier Science B.V. A ll rights reserved.