smoothness

1. (mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.Examples: "Smoothness can vary from 0 (for a nondifferentiable function) to infinity (for a smooth function)."countableuncountable

2. (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.Examples: "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 #92;mathbbS¹ is described by the modulus of smoothness, defined by the forward difference."countableuncountable