Definition:Truncation Error

Definition

A truncation error is an error associated with limitations in the construction of approximations.

This may arise by:

the use of an approximation rule

terminating an iterative method before it has converged

approximating a derivative by a difference

taking a finite number of terms of a power series expansion, for example a Taylor series

and so on.

It can also arise through truncation of a number.

Examples

Trapezoid Rule

Let the trapezoid rule be used to integrate $\cos x$ over the closed interval $\closedint 0 {0.8}$ using $8$ subintervals of length $0.1$.

Because $\size {\map{f} x} \le 1$, the truncation error cannot exceed a value given by:

$E \le \size {\dfrac {\paren {0.1}^2 \times 0.8} {12} } = 0.00067$

Also see

• Results about truncation errors can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): error: 1. (in numerical computation) Truncation errors
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): error: 1. (in numerical computation) Truncation errors