Variant Definitions
The IEEE standard does not define the terms machine epsilon and unit roundoff, so people are free to use different meanings which can cause some confusion.
The definition given here for machine epsilon is the one used by LAPACK and by James Demmel, a student and colleague of the primary architect for the IEEE standard, Prof. William Kahan. Most numerical analysts use the words machine epsilon and unit roundoff interchangeably and with this meaning.
Sometimes machine epsilon means the spacing of floating point numbers with zero exponent. By this definition, equals the value of the unit in the last place relative to 1, i.e., the distance from 1.0 to the next largest floating point number, and then for the round-to-nearest kind of rounding procedure, u. Prof. Nicholas Higham uses this scheme of definitions. The MATLAB eps function returns this, not the unit roundoff.
Read more about this topic: Machine Epsilon
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