Whats the relevance of the base-10 logarithmic plot?
There are many ways to measure error. Depending on what the focus is (do you want to measure “goodness” or “badness”?) one should pick a measure that is diagnostic for the object to be studied. Usually when studying convergence behavior it is common in mathematics to look at the maximum error and try to minimize it. The idea is: given that it is a maximum error, if you can minimize or manage that, then you can control the convergence, because all other errors are even smaller. This is the approach to control “badness” and minimize it to ensure the quality of the approximation or convergence. The point of the base-10 log plot of the relative error measures “goodness” of the approximation. The approximations shown here are so good that the curves on the left comparison plots appear like “on top of one another”. It is impossible to see the quality of the approximation because they are virtually identical. So to measure the quality of the approximation we have to “zoom in”, and given that
