Re: Odd behavior?
- To: mathgroup at smc.vnet.net
- Subject: [mg101859] Re: [mg101850] Odd behavior?
- From: Andrzej Kozlowski <akozlowski at gmail.com>
- Date: Mon, 20 Jul 2009 05:59:39 -0400 (EDT)
- References: <200907191115.HAA20885@smc.vnet.net> <116C8A49-E5B3-4CF1-BCCA-9FA60190C327@mimuw.edu.pl>
Just one more comment: in my below I carelessly used MachinePrecision and $MachinePrecision as interchangeable, which they are not. $MachinePrecision is a global constant whose value depends on your processor; MachinePrecision is a symbol used to refer to the precision of floating point computations performed by your processor. Andrzej Kozlowski On 19 Jul 2009, at 22:10, Andrzej Kozlowski wrote: > First and above all you have to understand that the results you are > getting have (essentially) nothing to do with Mathematica. You are > doing computations with MachinePrecision which means that they area > all performed entirely by your processor and Mathematica is only > reporting the results. So if you want to blame someone for these > "poor solutions" your choice is: > > 1. Processor makers for making binary (rather then decimal) > processors which cannot represent these decimal fractions with > perfect accuracy > 2. The laws of numerical analysis, which cause the order of > computations to matter in doing this sort of inexact arithmetic > > If you are not looking for someone to blame you could follow the > common advice in such situations and read the manual (as well as > looking into to an introductory text on basic numerical analysis, > particularly the section on binary representation of numbers with > finite precision). > > As for Mathematica: there are only a few bits of information > relevant to this. One is that it is Precision rather than Accuracy > that gives you relevant information, and your case the Precision is > always the same: $MachinePrecision. If the precision is > $MachinePrecision then Accuracy is defined purely formally as > $MachinePrecision-Log[10,Abs[x]] and carries no useful information > beside what is already included in the value Abs[x]. (In other > words, reporting the value of your computation and its Accuracy you > were simply reporting the same thing twice). > > The second useful piece of information is that: > > Chop[5.1 - 4.5 - 0.6] > 0 > > Andrzej Kozlowski > > > On 19 Jul 2009, at 04:15, elliot wrote: > >> The expression 5.1 - 4.5 - 0.6 gives different answers depending on >> the version of Mathematica. Version 6 says 0. (which is obviously >> what we expect) with an accuracy of about 307. Version 7 says >> -3.33067x10^-16 with an accuracy of about 31. Also, in version 7, >> if the expression is changed to 5.1 - (4.5 + 0.6) the answer it >> gives is 0. with an accuracy of about 307. Both versions were run >> on three different computers. >> >> Anybody know what changed or what I can do to prevent such poor >> solutions (besides forcing a specific order of evaluation)? Thanks. >> >
- Odd behavior?
- From: elliot <firstname.lastname@example.org>
- Odd behavior?