Convergence and error estimate of cascade algorithms with infinitely supported masks in L p (ℝ s )

Abstract

The cascade algorithm plays an important role in computer graphics and wavelet analysis. In this paper, we first investigate the convergence of cascade algorithms associated with a polynomially decaying mask and a general dilation matrix in Lp(ℝs) (1 ⩾ p ⩾ ∞) spaces, and then we give an error estimate of the cascade algorithms associated with truncated masks. It is proved that under some appropriate conditions if the cascade algorithm associated with a polynomially decaying mask converges in the Lp-norm, then the cascade algorithms associated with the truncated masks also converge in the Lp-norm. Moreover, the error between the two resulting limit functions is estimated in terms of the masks.