Can anyone explain how is actually used the backward error analysis in practice?
For example the forward analysis can give me a bound on the output of the error, the derived bound could be used in practice (i.e. implemented) to test if an implementation of a given algorithm is correct, can be the backward be used for the same purpose?
I know that basically the backward error analysis measures the error in terms of deviation of the inputs in real arithmetic to have the same output as the implementation using machine arithmetic. However I'm struggling to understand how such measure can be useful in practice.
