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)
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—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)