A Study Of The Approximation Property Of A Kind Of Spline Wavelets Interpolation And It's Parallel Algorithm

Because of it's specialties of adaptivness, multi-levels, compact support and semi-orthogonality, the spline wavelets have increasingly show his ability in solving PDEs. Here we obtain the best approximation property of spline wavelets interpolation in researching the spline wavelets to approximating the functions in Sobolev Spaces. Then we deduce the parallel algorithm of spline wavelets decomposition. That is to say, we can calculate the coefficients of scale functions in scale space V0 and wavelets in every wavelets space Wj simultaneously. Beginning with the one dimension Sobolev Space, we have discussed how the parallel algorithm operate in the spaces where simple node spline wavelets interpolation, cubic double spline wavelets interpolation, quintic double spline wavelets interpolation respectively exist. Finally, we prolongate the theory to two dimension tensor product wavelets space, proofing the best approximation property of product spline wavelets interpolation and constructing the parallel algorithm of the wavelets decomposition. The algorithm which constructs the parallel arithmetic of wavelets decomposition in the Sobolev Spaces with null boundary make it is possible for us to compute the coefficients of scale functions and wavelets functions in every layer, moreover, we can predict the error of the calculation and the layer that the calculation will proceed.