On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation

The Deslauriers-Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers-Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l_∞-stability bounds for the multiresolution transform. A variety of tests indicate that these l_∞ bounds are closer to numerical estimates than those obtained with other approaches.