smoothnesses

Noun

smoothness (countable and uncountable, plural smoothnesses)

1. The condition of being smooth; the degree or measure of said condition.
   • The admirable smoothness of the riding also reflected the greatest credit on those who, despite the difficulties caused by the shortage of men and materials, have succeeded in maintaining the track in such first-class order.1946 July and August, Cecil J. Allen, “British Locomotive Practice and Performance”, in Railway Magazine, page 213
2. The highest order of derivative (the differentiability class) over a given domain.
   • Smoothness can vary from 0 (for a nondifferentiable function) to infinity (for a smooth function).
3. (approximation theory, numerical analysis) The quantity measured by the modulus of smoothness.
   • 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....2013, Feng Dai, Yuan Xu, Approximation Theory and Harmonic Analysis on Spheres and Balls, Springer, page 79