The approximation error of an approximation 
to a mathematical object 
is the difference
 |
For scalar quantities, the absolute error is 
and, when 
,
the relative error is
 |
For vectors, functions, and other objects in a normed space, the error is commonly
measured by 
.
An error bound is a proved upper bound for one of
these quantities. Approximation error should be distinguished from roundoff
error, which is introduced by finite-precision arithmetic.
