3 ms·
You should be okay with a sum but interval arithmetic can blow up in a way that is not correlated with the numerical accuracy of the algorithm. Newton's method,
by nestorD 5y ago
You should be okay with a sum but interval arithmetic can blow up in a way that is not correlated with the numerical accuracy of the algorithm.
Newton's method, for example, is strongly convergent but produces diverging intervals.
- uyt 5y agoWhy does that happen? Is it because the errors are in opposite directions and will cancel each other out?
- nestorD 5y agoThat (and overall the unability to take correlation between error into account) and the fact that intervals propagated are upper bounds for some things like the division.
- rjmunro 5y agoYou can use other algorithms in these cases, and you can do things like converge your interval on a result by testing different values and seeing if the result is above the root or below the root, (or if it's within the error, so not possible to determine).