Numerical error

In software engineering and mathematics, numerical error is the error in the numerical computations.

Time series of the Tent map for the parameter m=2.0 which shows numerical error: "the plot of time series (plot of x variable with respect to number of iterations) stops fluctuating and no values are observed after n=50". Parameter m= 2.0, initial point is random.

Types

It can be the combined effect of two kinds of error in a calculation. The first is referred to as round-off error and is caused by the finite precision of computations involving floating-point numbers. The second, usually called truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.

Measure

Floating-point numerical error is often measured in ULP (unit in the last place).

See also

• Loss of significance
• Numerical analysis
• Error analysis (mathematics)
• Round-off error
• Kahan summation algorithm
• Numerical sign problem

References

• Accuracy and Stability of Numerical Algorithms, Nicholas J. Higham,
• "Computational Error And Complexity In Science And Engineering", V. Lakshmikantham, S.K. Sen,