Definition of "smoothness" noun countable and uncountable , plural smoothnesses
The condition of being smooth ; the degree or measure of said condition . quotations examples
Quotations The ‘smoothness ’ of distributions can be understood in various senses , this is why we used quotation marks before ; further we will drop them . The smoothness can be understood as the differentiability of the distribution function , boundedness of some of its derivatives , the existence of the absolutely continuous component , the decrease of the characteristic function with a certain rate , the validity of the Cramér condition , the condition σ ( Φ ) → 0 {\displaystyle \sigma (\Phi )\rightarrow 0} as n → ∞ {\displaystyle n \rightarrow \infty } , etc .
1998, Vladimir V. Senatov, Normal Approximation: New Results, Methods and Problems, Walter de Gruyter (VSP), page 32
(approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness . quotations examples
Quotations A central problem in approximation theory is to characterize the best approximation of a function by polynomials , or other classes of simple functions , in terms of the smoothness of the function . In this chapter , we study the characterization of the best approximation by polynomials on the sphere . In the classical setting of one variable , the smoothness of a function on S 1 {\displaystyle \mathbb {S } ^{1}} is described by the modulus of smoothness , defined by the forward difference .
2013, Feng Dai, Yuan Xu, Approximation Theory and Harmonic Analysis on Spheres and Balls, Springer, page 79