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On 08/04/2011 11:23 AM, N.M. Maclaren wrote:
And, lastly, when numeric programmers and their users are given a choice between deterministic results and much faster execution, they choose the latter every time.
So would I do, especially in interval computations. Deterministic results serve no purpose if the result is guaranteed to be correct
and reasonably accurate. Whether a computed enclosure is [1.23456,1.23567] or [1.23455,1.23566]is irrelevant for interval computations, since the width indicates already uncertainty in the third decimal place after the dot.
The requirement that both enclose the true range is essential, and sufficient if the overestimation is not too large.
Arnold Neumaier