Topics: Numerical Analysis - Error

Let and be two exact values, and and , their respective approximate values; and have the errors and .

That is:

Effect on Addition and Subtraction

The effect of the errors on addition and subtraction is:

Notice that, effectively, the errors are added when both adding and subtracting and with their approximate values.

Effect on Product and Division

In the case of the product, we have that:

If the approximate values and are greater that , then the error will grow in a significative way.

Given and good approximations, we can show that the relative error of the product of two numbers is approximately the sum of the relative errors of the individual approximations: