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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
anytime algorithm
An algorithm that returns a sequence of
approximations to the correct answer such that each
approximation is no worse than the previous one, i.e. the
algorithm can be stopped at _any time_.
Newton-Raphson iteration applied to finding the {square
root} of a number b is another example:
x = (x + b / x) / 2
Each new x is closer to the square root than the previous one.
Applications might include a real-time control system or a
chess program that is allowed a fixed thinking time.
(2007-06-19)