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BUILT-IN MATHEMATICA SYMBOL

$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.

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:

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Do a computation with fixed 20-digit precision:

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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: