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$MinPrecision

$MinPrecision
gives the minimum number of digits of precision to be allowed in arbitrary-precision numbers.
  • Positive values of $MinPrecision make Mathematica pad arbitrary-precision numbers with zero digits to achieve the specified nominal precision. The zero digits are taken to be in base 2, and may not correspond to zeros in base 10.
  • $MinPrecision is measured in decimal digits, and need not be an integer.
Make sure precision is kept at or above machine precision in a calculation:
Do a computation with fixed 20-digit precision:
Make sure precision is kept at or above machine precision in a calculation:
In[1]:=
Click for copyable input
Out[1]=
 
Do a computation with fixed 20-digit precision:
In[1]:=
Click for copyable input
Out[1]=
Power method for the largest eigenvalue using fixed precision:
Find the largest eigenvalue of the 4×4 Hilbert matrix to 47 digits:
Without fixed precision the result indicates lost precision:
The fixed precision is correct to 47 digits since the iteration is self-correcting:
$MinPrecision does not affect parts of computations with machine numbers:
If needed, use SetPrecision to eliminate machine numbers from the input:
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