Interpretation of PrecisionGoal and AccuracyGoal
- To: mathgroup at smc.vnet.net
- Subject: [mg80684] Interpretation of PrecisionGoal and AccuracyGoal
- From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
- Date: Wed, 29 Aug 2007 04:10:08 -0400 (EDT)
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?