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3 votes
0 answers
469 views

Stable and fast computation of the squared euclidean distance matrix

Let's say I want to compute the matrix M of the squared euclidean distances between each pair of vectors (x,y) belonging to two sets X and Y respectively. The sets of vectors X and Y have …
4 votes
2 answers
688 views

Proof that (x-y)(x+y) is more accurate than x²-y²

I was carrying on my reading of What Every Computer Scientist Should Know About Floating-Point Arithmetic but got stuck on the proof of Theorem 2 (page 34). At some point it says: \begin{align} (x \o …
3 votes
1 answer
142 views

Proof that a guard digit bound the error of subtraction

I was reading What Every Computer Scientist Should Know About Floating-Point Arithmetic, which is extremely interesting. But I have some troubles understanding the proof of Theorem 9 (page 33). First …