I'm currently working on numerical equation solving algorithms, which is basically the same as finding the roots of a function. It happens that the roots where the function changes sign and the roots where the function does not change sign are found and approximated separately. Here is my problem: in mathematics, a root of a function is any value that evaluates to zero, whereas in computer sciences, the term "root" is used only when there is a sign change.
So the terminology makes sense for each domain but I would need specific terms for each type of root to be accurate and non-ambiguous, since "root with/without sign change" doesn't sound good at all. I would like to know if there are usual mathematical terms for this. I didn't find any on the Internet. I thought about "odd root" and "even root" to refer to the multiplicity (number of derivatives that evaluate to zero) but I've not seen this anywhere (except for polynomials maybe).
Terminology for roots with or without sign change
real-analysisrootsterminology
Best Answer
As far as roots where the given function changes sign on both sides, they may be found using bracketing methods. In contrast, roots which do not have this property are local extrema.
For smooth functions, these cases fall into even and odd roots as you've mentioned, but not all functions are smooth (e.g. $\sqrt[3]x$ or $|x|$) and thus cannot be classified into either case.
After having read a fairly large volume of literature concerning the case in which roots may be bracketed, I have not found any consistent terminology for these two classes of roots.
If I had to give them names however, I would classify them as bracketable roots and local extrema roots due to the context in which I would differentiate the two, which would be in relation to bracketing methods (root-finding algorithms) versus optimization algorithms.
From a more numerical analysis standpoint, I've never heard the claim that roots which do not experience a sign change should not be classified as a root and certainly have seen discussions concerning the "local extrema roots".