Question

Difference between round off error and truncation error

Answer 1

◆ Round off error is the error caused by approximate representation of numbers.

When people talk about round off error, it is the error between the number and its representation.

● For example 200/3 would be represented as 66.6667 in a six significant digit computer that rounds off the last digit. The last digit has been rounded up from 6 to a 7. The difference between 200/3 and 66.6667, that is, 200/3-66.6667 is the round off error.

◆ Truncation error is error caused by truncating a mathematical procedure.

● Examples of truncation error abound and include

● In exact differentiation, you need dx approaching zero; in numerical differentiation we can only choose dx=finite.

● In exact integration, one would need infinite number of trapezoids to find the integral; in numerical integration, we can only choose a finite number of trapezoids.

● In the Maclaurin series for transcendental and trigonometric functions, we need infinite number of terms for exact solution; in a numerical solution, we can only choose finite number of terms.

●● In short Round off error is caused by representing numbers approximately; Truncation error is caused by approximating mathematical procedures.

Hope it helps you..

Answer 2

Difference between round off error and truncation error  is as follows:

• In a numerical computation, each number must be rounded to a certain number of digits. On this fact, round- off error depends. It is caused by truncating a mathematical procedure.
• At the time, finite process replaces infinite one, truncation errors. Approximating mathematical procedures cause this error. It has two types in case of numerical integration, these are global and local truncation errors.