Nonuniform cascade algorithms

Abstract

For a sequence of bounded linear operators Hk, k=0,1,..., on a Banach space S, the algorithm φk,n=Hkφk+1,n-1 generates a family of sequences (φk,n)n=0 ∞,k=0,1,..., from an initial family of vectors φk,0∈S,k=0,1,.... We study the convergence of φk,n as n→∞, and give an application on the convergence of cascade algorithms for nonuniform splines when S is the space of all sequences φ(φi)i∈Z with norm ∥φ∥supi∈Z∥φi∥