The second order modulus revisited: remarks, applications, problems
Heiner Gonska, Ralitza Kovacheva
Abstract
Several questions concerning the second order modulus of smoothness are addressed in this note. The central part is a refined analysis of a construction of certain smooth functions by Zhuk and its application to several problems in approximation theory, such as degree of approximation and the preservation of global smoothness. Lower bounds for some optimal constants introduced by Sendov are given as well. We also investigate an alternative approach using quadratic splines studied by Sendov.
Topics & Concepts
SmoothnessMathematicsQuadratic equationApplied mathematicsOrder (exchange)Degree (music)ModulusConstant (computer programming)ModuliModulus of continuityThird orderMathematical optimizationMathematical analysisComputer scienceType (biology)GeometryPhysicsEconomicsGeologyPaleontologyFinanceProgramming languageAcousticsQuantum mechanicsPhilosophyTheologyApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationMathematical functions and polynomials