Applications of Linear Approximation and Accuracy
Note, x - a is often symbolized by Δx
Dealing with Linear Approximation, we are dealing with calculations that are… approximate. In this there is a margin for error, and some results are more accurate than others.
Definition - Linear Approximation Error
If the variable x-value is measured as x = a, with the error as Δx (or x - a) units, then the Δf can be the error in estimating our f(x),
Δf = f(x) - f(a) =roughly= f’(a)Δx
Linear Approximation Cube
Linear Approximation Error
Linear Approximation Error
Relative Error and Percentage Error
What we have been working with above is the absolute error. This gives, as the name suggests, the pure value of the error. However, it is not an error value comparable between different types of measurements. For example, an error when measuring the distance between two cities of 1 meter, is not the same as a an error of measuring shoe size of 1 meter. This is where we introduce Relative Error and Percentage error, to give us a better understanding of the relevance of error.
Definition - Relative Error
Definition - Percentage Error
Percentage Error is simply Relative Error as a Percentage
Relative Error
