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In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties ... For example, repeated multiplication, ...
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
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Condition numbers can also be defined for nonlinear functions, and can be computed using calculus.The condition number varies with the point; in some cases one can use the maximum (or supremum) condition number over the domain of the function or domain of the question as an overall condition number, while in other cases the condition number at a particular point is of more interest.
A more elegant way of writing the so-called "propagation of error" variance equation is to use matrices. [12] First define a vector of partial derivatives, as was used in Eq(8) above:
Statements about relative errors are sensitive to addition of constants, but not to multiplication by constants. For absolute errors, the opposite is true: are sensitive to multiplication by constants, but not to addition of constants. [5]: 34
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.