This is usually done using numerical approximation techniques.

Sparse approximation techniques have found wide use in applications such as image processing, audio processing, biology, and document analysis.

Ultimately, this approximation technique is a standard ingredient in the proof that simplicial homology groups are topological invariants.

The approximation techniques usually aren't very useful either, as they will require centralized control and, usually, predefined traffic demands.

The third task is therefore to find approximation techniques for achieving the desired responses.

Instead, approximation techniques, such as mean field approximations from statistical physics, or computer simulations are used to understand the behaviors of the system.

It covers modern computational methods, such as interpolations and approximation techniques and real-time computation.

A similar approximation technique by trigonometric functions is commonly called Fourier expansion, and is much applied in engineering, see below.

Complicated master equations which resist analytic treatment can be cast into this form (under various approximations), by using approximation techniques such as the system size expansion.

Kemper and Mandjes show that for some parameters these bounds are not tight and show demonstrate an approximation technique.