Re: back to the roots
George Corliss, replying to Bill Walster's comments on Exact Dot Prouct:
> I interpret Bill's point as asking, "If your input is good to three
> figures, then your answer is good to about three figures. How does
> a infinitely precise arithmetic provide useful information, when you
> should not pay any attention to digits 4 and beyond anyway?"
For linear problems, yes. The situation is different for non-linear
cases. If I take a square root, my relative precision actually improves
and I might get twice as many significant digits as in my input. Now
consider an algorithm that iteratively takes square roots followed by
an unwinding loop that effectively squares the results until it delivers
my answer. If I don't have VERY high precision at the deeper levels, I
will end up with ENTIRE as the best-known enclosure.
The EDP may be capable of dealing with these situations.
Michel.
---Sent: 2013-06-28 21:25:11 UTC