The Difference Between Rounding Error and Truncation Error Explained

Rounding errors occur when a numerical calculation must be rounded or trimmed to a certain number of digits. Truncation errors, on the other hand, arise when an infinite process is replaced by a finite one. This is done by cutting or rounding symmetrically, and the relative rounding error due to cutting is defined by I, e. The maximum relative rounding error due to cutting is given by 'd', which is the length of the mantissa and depends on the machine. The maximum relative rounding error due to symmetrical rounding is given by For a computer system with binary representation, the epsilon of the machine due to cutting and symmetrical rounding are given by. In numerical analysis and scientific computation, truncation error is the error caused by the approximation of a mathematical process. This can be seen when using a Reimann sum of two segments on the left with the same width of segments. The error caused by choosing a finite number of rectangles instead of an infinite number of them is a truncation error in the mathematical process of integration. Occasionally, by mistake, the rounding error (the consequence of using finite-precision floating-point numbers in computers) is also called a truncation error, especially if the number is rounded by cutting. Given an infinite series, the truncation error of x% 3d0,75 can be found if only the first three terms of the series are used. It is important to note that this is not the correct use of the truncation error; however, calling it by truncating a number may be acceptable. In conclusion, it can be seen that there are distinct differences between rounding errors and truncation errors. Rounding errors occur when a numerical calculation must be rounded or trimmed to a certain number of digits, while truncation errors arise when an infinite process is replaced by a finite one.