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:
“There are nine orders of angels, to wit, angels, archangels, virtues, powers, principalities, dominations, thrones, cherubim, and seraphim.”
—Gregory the Great, Pope (c. 540–604)
“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)