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Results tagged with numerical-analysis
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user 22833
4
votes
2
answers
688
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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 …
- 483
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 …
- 483
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 …
- 483