Re: Re: Accuracy and Precision

*To*: mathgroup at smc.vnet.net*Subject*: [mg37008] Re: [mg36982] Re: Accuracy and Precision*From*: David Withoff <withoff at wolfram.com>*Date*: Sun, 6 Oct 2002 05:32:53 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

> > The last part of my message you are quoting was completely wrong, as > > was pointed out by Allan Hayes. Mathematica does not track precision of > > machine arithmetic computations. In order for Mathematica to give > > reliable information about the precision of a computation you have to > > explicitly set the precision of all the numerical quantities. > > > > Your own example at the bottom simply shows you have not understood the > > evaluation mechanism of Mathematica. > > Just opposite, thanks to you and other participants, I completely > understood it. SetAccuracy just takes anything and calls it accurate. > This behavior is useless if not stupid. I am not sure I understand what you are referring to as "useless if not stupid." The main purpose of SetAccuracy is to allow people who have done their own error analysis to specify the numerical error in an input or in a result. It is often possible through careful numerical analysis, for example, to come up with a better error estimate than can be given by generic rules for propogation of error. Another common use of SetAccuracy is for converting machine numbers or exact numbers into variable-precision numbers in situations when it is desired that a calculation be done using variable-precision arithmetic. Is there some aspect of this that you think is "useless if not stupid", or was that remark referring to something else? Dave Withoff Wolfram Research