Re: Interpretation of PrecisionGoal and AccuracyGoal

*To*: mathgroup at smc.vnet.net*Subject*: [mg80850] Re: Interpretation of PrecisionGoal and AccuracyGoal*From*: Chris Chiasson <chris.chiasson at gmail.com>*Date*: Tue, 4 Sep 2007 03:44:17 -0400 (EDT)*References*: <fb39l4$q54$1@smc.vnet.net>

On Aug 29, 3:10 am, "Andrew Moylan" <andrew.j.moy... at gmail.com> wrote: > The article "ref/PrecisionGoal" in the Mathematica documentation says: > > ---- > With PrecisionGoal->p and AccuracyGoal->a, Mathematica attempts to make the > numerical error in a result of size x be less than (10^-a)+|x| 10^-p. > ---- > > On the other hand, the article at > "tutorial/NIntegrateIntegrationStrategies#280704764" says: > > ---- > "GlobalAdaptive" stops if the following expression is true: > globalError<=globalIntegral 10^-pg \[Or] globalError<=10^-ag > ---- > > So GlobalAdaptive has a different interpretation of the meaning of > PrecisionGoal and AccuracyGoal than that given in the article > "ref/PrecisionGoal". > > Which of these two interpretations is dominant in Mathematica's actual > numerical methods? Or does it vary from method to method? I am interested in knowing this also. The documentation seems to be self-contradictory because it says: Under ref/AccuracyGoal (and ref/PrecisionGoal): "With AccuracyGoal->a and PrecisionGoal->p, Mathematica attempts to make the numerical error in a result of size x be less than (10^-a) + | x| 10^-p." ... "Find a minimum with convergence criteria |x_k-xstar| <= max(10^-10,| x_k| 10^-8) and del f(x_k) <= 10^-10" "f[x_]=Sin[x^2];" "FindMinimum[f[x],{x,2},AccuracyGoal->10,PrecisionGoal->8]" Under ref/FindMinimum: "FindMinimum continues until either of the goals specified by AccuracyGoal or PrecisionGoal is achieved." I emailed WRI about this a while back and never received a response [ WR #875035 ].