There are algorithms that have errors along the lines of
n (log(n) eps)^i
where I assumed that |x_i| ~ 1, and \sum x_i ~ 1, which is what I was
looking into. With this I can go to n \eps^{-1}.
But maybe something like BigFloat would be more practical. I'll look into
that as well -
On Tuesday, February 3, 2015 at 4:48:20 AM UTC-5, Christoph Ortner wrote:
On Monday, 2 February 2015 16:59:19 UTC, Steven G. Johnson wrote:
It might be nice to submit a patch to OpenBLAS to make their dot
functions use pairwise summation; this is almost as accurate as KBN
summation but
On Tuesday, February 3, 2015 at 4:48:20 AM UTC-5, Christoph Ortner wrote:
For my own applications, I really need something much better than pairwise
summation, which has ~\eps \sum |x[i]| error, so I will try this, but I'm
afraid your syntax goes over my head. I suppose, this would require
On Monday, 2 February 2015 16:59:19 UTC, Steven G. Johnson wrote:
It might be nice to submit a patch to OpenBLAS to make their dot functions
use pairwise summation; this is almost as accurate as KBN summation but
with negligible performance penalty (for a large base case), so it should
be
It might be nice to submit a patch to OpenBLAS to make their dot functions
use pairwise summation; this is almost as accurate as KBN summation but
with negligible performance penalty (for a large base case), so it should
be possible to put together an attractive pull request.
For Base,
If you wanted to implement such an algorithm, you would need to robust-ify
the multiplication as well, using a two-product style algorithm: this
paper goes into a lot of detail:
http://www.ti3.tu-harburg.de/paper/rump/OgRuOi05.pdf
Alternatively, you could use full double-double arithmetic: see
I realise I didn't actually answer your question: I can't speak as to
whether it will be accepted in Base (you will probably have to open an
issue or pull request to start a discussion), but at the very least it
would be useful to at least have in a package somewhere. If you don't want
to
thanks for the suggestions; indeed, Rumpf's paper is my main reference :)
for these things.
many thanks - well I will implement it first of all, and then see where it
could go.
Christoph
