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.