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:
“What is all wisdom save a collection of platitudes? Take fifty of our current proverbial sayings—they are so trite, so threadbare, that we can hardly bring our lips to utter them. None the less they embody the concentrated experience of the race and the man who orders his life according to their teaching cannot go far wrong.”
—Norman Douglas (1868–1952)