Abstract
This paper establishes an equivalent relation between the convergence of a cascade algorithm in Sobolev space and the convergence of an associated cascade algorithm in Lp space. It reduces the convergence in Sobolev space to that in Lp space. On the other hand, by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in Sobolev space. It is very easy to implement the algorithm. Examples are given to illustrate the theory.
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