Truncation Error and Rounding Error (numerical analysis)¶
Definition¶
In numerical analysis, we have computational error. And we can subdivide this computational error into truncation error and rounding error.
Truncation Error¶
The resulting approximation due to truncating an infinite series, deplacing derivatives by finite differences, or terminating an iterative sequence before convergence.
Rounding Error¶
The difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounding arithmetic.
By definition, computational error is the sum of truncation and rounding error.
Roughly speaking, rounding error tends to dominate in purely algebraic problems with finite solution algorithms. And truncation error tends to dominate in problems involving integrals, derivatives, or nonlinearities, which often require an infinite process to be truncated.