truncation error
Definition
Noun: 1. (Mathematics, Computing) An error that occurs when a numerical calculation or series is terminated (truncated) after a finite number of steps or digits, before it is mathematically complete. This results in an approximation that differs from the true, infinite-precision value.
Usage
This term is used primarily in technical contexts involving numerical analysis, scientific computing, and computer programming. It describes the inherent inaccuracy introduced by using a finite process to represent an inherently infinite one.
Examples
- The difference between the infinite Taylor series for the exponential function and its approximation using only the first five terms is a truncation error.
- When the simulation stopped the iterative calculation after 1000 cycles, a small truncation error remained in the final result.
- Programmers must be aware of truncation error when using numerical methods to solve differential equations.
Advanced Usage
- Error Analysis: Truncation error is a key concept in error analysis, often contrasted with round-off error (the error from representing numbers with a finite number of digits).
- Order of Error: The rate at which truncation error decreases as more terms are used or step size is reduced (e.g., O(h²)) is a critical measure of a numerical method's efficiency.
Variants and Related Words
- Truncate (verb): To shorten by cutting off a part. In computing, to limit the number of digits in a number without rounding.
- Discretization Error: A closely related type of error arising from converting continuous models or equations into discrete, solvable steps, often involving truncation.
Synonyms
- Approximation error (in this specific context)
- Cut-off error
Antonyms
- Exact value
- Closed-form solution (a solution expressible in a finite number of standard operations)
Noun
-
(mathematics) a miscalculation that results from cutting off a numerical calculation before it is finished
