6533b82ffe1ef96bd12948d9

RESEARCH PRODUCT

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

Rosa DonatSergio AmatJ. Carlos Trillo

subject

PolynomialApplied MathematicsMathematical analysisLagrange polynomialStability (probability)Polynomial interpolationsymbols.namesakeOperator (computer programming)Piecewise Lagrange interpolationsymbolsPiecewiseStabilityLinear multiresolutionAnalysisNumerical stabilityInterpolationMathematics

description

Abstract 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.

yearjournalcountryeditionlanguage
2009-10-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2009.04.038