Relative Error Analysis

Consider the system , in practice we may not always have the exact values for . We may instead have something like where represents error, in this case it would be useful to analyze how slight changes in affect . This is Error Analysis.

To represent a system with error we can write it as such:

We can simplify this to get the direct relation:

To achieve relative error analysis we want to study the following:

To quantify this we use Vector Norms we will also introduce the Condition Number to get the following relation:

This relation describes how relative changes in affect relative changes in .