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.