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AccuracyGoal

AccuracyGoal
is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result.
MORE INFORMATION
  • AccuracyGoal->Infinity specifies that accuracy should not be used as the criterion for terminating the numerical procedure. PrecisionGoal is typically used in this case.
  • Even though you may specify AccuracyGoal->n, the results you get may sometimes have much less than n-digit accuracy.
  • AccuracyGoal effectively specifies the absolute error allowed in a numerical procedure.
  • With AccuracyGoal->a and PrecisionGoal->p, Mathematica attempts to make the numerical error in a result of size be less than .
EXAMPLESCLOSE ALL
Basic Examples   (2)
Approximate a numerical integral to at least 8 digits of accuracy:
Use precision (relative error) as the basis for error control in solving an ODE:
The relative error is small:
Without specifying the AccuracyGoal, the relative error is much larger:
Approximate a numerical integral to at least 8 digits of accuracy:
In[1]:=
Click for copyable input
Out[1]=
 
Use precision (relative error) as the basis for error control in solving an ODE:
In[1]:=
Click for copyable input
Out[1]=
The relative error is small:
In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
Out[3]=
Without specifying the AccuracyGoal, the relative error is much larger:
In[4]:=
Click for copyable input
Out[4]=
Scope   (2)
Find a minimum with convergence criteria and :
Use convergence criteria and :
Use convergence criteria and not possible at machine precision:
Use a higher working precision to allow convergence:
Solve a differential equation using high-precision arithmetic:
Use AccuracyGoal and PrecisionGoal at half the 32-digit working precision:
This corresponds to the automatic setting used by NDSolve:
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