Sentence examples for smooth functions from inspiring English sources

for the smooth functions,.

are nonnegative smooth functions on.

Let be nonnegative smooth functions on.

C ∞ = ⋃ k ≥ 0 C k (smooth functions) and C c ∞ denotes smooth functions with compact support.

Convex functions, smooth functions, piecewise linear functions, convex and concave functions, and sub-smooth functions are examples of semi-smooth functions.

The coefficients, are sufficiently smooth functions of in, where, and,.

The smooth functions are used in place of discontinuous functions.

Major design criteria in the smooth functions used is a common smoothing factor which combines common elementary functions to approximate the original non-smooth functions.

Moreover, we prove that the minimum of the optimization problem can be approximated by smooth functions.

In particular, we prove that deep ReLU networks more efficiently approximate smooth functions than shallow networks.

Standard wavelet linear approximations generate oscillations (Gibbs' phenomenon) near singularities in piecewise smooth functions.