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:
“One cannot be a good historian of the outward, visible world without giving some thought to the hidden, private life of ordinary people; and on the other hand one cannot be a good historian of this inner life without taking into account outward events where these are relevant. They are two orders of fact which reflect each other, which are always linked and which sometimes provoke each other.”
—Victor Hugo (1802–1885)
“God is a foreman with certain definite views
Who orders life in shifts of work and leisure.”
—Seamus Heaney (b. 1939)