Smoothness

Quick meaning: Smoothness is a noun meaning The condition of being smooth; the degree or measure of said condition.

Meaning

The condition of being smooth; the degree or measure of said condition.

More Meanings

1. (mathematical analysis, of a function) The highest order of derivative (the differentiability class) over a given domain.
2. (approximation theory, numerical analysis, of a function) The quantity measured by the modulus of smoothness.

Example Sentences

Smoothness can vary from 0 (for a nondifferentiable function) to infinity (for a smooth function).

With it,^([a pavement profile]) paving operations can be adjusted "on the fly" to maintain or improve smoothness.

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.

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.

Word Forms

• smoothnesses

Antonyms for smoothness

Common opposites include jerkiness, roughness.

Related Words

Related dictionary entries include softness, soft, delicacy, gentleness, kindness, sweetness.

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