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 words orders of and/or orders:
“Your money’s no good here. Orders of the house.”
—Stanley Kubrick (b. 1928)
“Punishment may make us obey the orders we are given, but at best it will only teach an obedience to authority, not a self-control which enhances our self-respect.”
—Bruno Bettelheim (20th century)