In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth order approximation, a first order approximation, a second order approximation, and so forth.
Formally, an nth order approximation is one where the order of magnitude of the error is at most, or in terms of big O notation, the error is In suitable circumstances, approximating a function by a Taylor polynomial of degree n yields an nth order approximation, by Taylor's theorem: a first order approximation is a linear approximation, and so forth.
The term is also used more loosely, as detailed below.
Famous quotes containing the word orders:
“He was thoughtful and grave—but the orders he gave
Were enough to bewilder a crew.
When he cried “Steer to starboard, but keep her head larboard!”
What on earth was the helmsman to do?”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)