Why is rewriting $x^2 -y^2$ as $(x+y)(x-y)$ a way to avoid catastrophic cancellation? We are still doing $(x-y)$. Is it because the last operation in the second form is a multiplication?
Given three points or vectors in the plane: \begin{align} \vec a &= (a_x,a_y) \\ \vec b &= (b_x,b_x) \\ \vec c &= (c_x,c_y) \end{align} How do you compute $\lVert \vec c - \vec a \rVert - \lVert \vec b - \vec a \rVert$, i.e. "how much farther is it from $\vec a$ to $\vec c$ than from ...
It was recently mentioned in chat that the tag-info for the tag catastrophic-cancellation consists basically only of a few links. I have tried to improve it at least a bit, but it would be probably better if somebody who know more about numerical mathematics had a look at the tag-info. (And there...
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