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Groups > comp.soft-sys.math.mathematica > #1520
| From | Richard Fateman <fateman@cs.berkeley.edu> |
|---|---|
| Newsgroups | comp.soft-sys.math.mathematica |
| Subject | Re: why extending numbers by zeros instead of dropping precision is a good idea |
| Date | 2011-04-07 12:06 +0000 |
| Organization | Steven M. Christensen and Associates, Inc and MathTensor, Inc. |
| Message-ID | <ink9b8$gad$1@smc.vnet.net> (permalink) |
On 4/4/2011 3:30 AM, Noqsi wrote: > On Apr 1, 1:34 am, Bill Rowe<readn...@sbcglobal.net> wrote: > >> It seems FixedPoint is doing something behind the scene that >> avoids the problem you describe above. > > Well, of course, a specialized function can use specialized error > estimation methods. > FixedPoint can be written in about one line. It needs a stopping criterion, SameTest which in Mathematica can be any function you choose or the system's mysterious "automatic". There is probably nothing much special in the default SameTest. I expect it is something like SameTest[x0_,x1_]:= Abs[(x1-x0)] < Abs[x0]*10^(Precision[x0]) ;; we assume x0 is not zero; else use x1 on rhs; If they are both zero, obviously the fixed point has been reached... I suspect this test is best executed in fixed precision, but maybe it doesn't matter much.
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Re: why extending numbers by zeros instead of dropping precision is a good idea Richard Fateman <fateman@cs.berkeley.edu> - 2011-04-07 12:06 +0000
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