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More news of accurate floating-point summation
A posting by Siegfried Rump this morning on the reliable_computing
list announced a followup to the paper that I reported to this
list on Tue, 22 Nov 2005 17:45:08 -0700 (MST):
...
The second ones will be published in
S.M. Rump, T. Ogita, and S. Oishi. Accurate Floating-Point Summation.
41 pages, submitted for publication, 2006
and give a result of accuracy eps^2 , independent of the condition
number! Again only double precision operations are used. Although
always accurate to the last bit, the algorithms are for condition
numbers up to eps^-1 again some 40 % faster than XBLAS.
...
His Web site at
http://www.ti3.tu-harburg.de/publications/rump
points to the new paper:
http://www.ti3.tu-harburg.de/paper/rump/Ru05d.pdf
Here is a BibTeX reference from fparith.bib for the report:
@TechReport{Rump:2005:AFP,
author = "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
Oishi",
title = "Accurate Floating-Point Summation",
type = "Technical Report",
number = "05.12",
institution = "Faculty for Information- and Communication Sciences,
Hamburg University of Technology",
address = "Hamburg, Germany",
day = "13",
month = nov,
year = "2005",
bibdate = "Wed Jan 04 12:31:28 2006",
URL = "http://www.ti3.tu-harburg.de/paper/rump/Ru05d.pdf";,
acknowledgement = ack-nhfb,
}
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