Talk:Binary splitting

Revision
The revision with comment
 * (fast multiplication does not move the bulk of the computation into the domain of multiplication; the binary splitting algorithm does, fast multiplication ensures that this is an advantage)

changed the text of the article from
 * The advantage of binary splitting comes from moving the bulk of the computation into the domain of multiplication using fast algorithms like Schönhage-Strassen.

to
 * The advantage of binary splitting comes from moving the bulk of the computation into the domain of multiplication and using fast algorithms like Schönhage-Strassen.

I think that this wording is awkward and expresses the idea less accurately than the older version. I admit that it is possible that the comment has relevance, though. Are there any suggestions for dealing with these issues? If there's no feedback I'm likelu to revert. CRGreathouse (talk | contribs) 06:29, 16 August 2006 (UTC)

Karatsuba's FEE method
I reverted this page to an earlier version (dated April 2007) to avoid references to E. Karatsuba's FEE method that don't belong here - they should be on a separate page. Rpbrent 05:31, 22 September 2007 (UTC)


 * Your note isn't OK: Haible/Papanikolaou paper consists from the E.Karatsuba results represented in slightly different form (if to speak about method of calculation), the Gordon page contains also invalid information about the origin of the Binary Splitting method. There is no any fast method for calculation of sums of series which is called "Binary Splitting", there is only one method for fast calculation of sums of series of a special form --- the FEE. If somebody uses the FEE process with wrong reference to the Binary Splitting --- this is a wrong information which must be corrected. That is why I will give the information about the FEE. I'd like to remark that in the paper [1] of Lozier/Olver (Institute of Standards and Technology of U.S.A.) the method for fast summing up is called EKar'91, not the FEE, (because the authors refereed to the E. Karatsuba main paper of 1991).
 * Ekatherina Karatsuba —Preceding unsigned comment added by 212.48.130.180 (talk • contribs)


 * [1]Lozier, D.W. and Olver, F.W.J. Numerical Evaluation of Special Functions. Mathematics of Computation 1943-1993: A Half -Century of Computational Mathematics, W.Gautschi,eds., Proc. Sympos. Applied Mathematics, AMS, v.48, pp.79-125 (1994).


 * I agree that Karatsuba's FEE method should be its own separate article. Oleg Alexandrov (talk) 15:58, 23 September 2007 (UTC)

Statements
I deleted the wrong statements: "Binary splitting is used by the fastest existing software for computing mathematical constants such as π and e to high accuracy. It can be used more generally to evaluate many common special functions of arbitrary arguments; however, it is mainly useful when the argument is a small rational number. ". The "Binary Splitting" method for computing mathematical constants such as π and e to accuracy of $$N$$ digits has the complexity bound  $$~ N^2$$ -- it's easy to calculate it according to formulas presented at the "Binary Splitting"- Wiki page. The fastest existing software for computing mathematical constants such as π and e to high accuracy based on the Fast E-functions Evaluation Method (the FEE, 1990) and has the complexity bound $$~ N^{1+\epsilon}$$.

See

http://math.nist.gov/mcsd/Reports/2001/nesf/node35.html

http://math.nist.gov/mcsd/Reports/2001/nesf/

http://math.nist.gov/stssf/

the method is called "Kar'91" there.

See also

http://www.ccas.ru/personal/karatsuba/algen.htm

http://www.ccas.ru/personal/karatsuba/faqen.htm

the method is called the FEE there.

--147.231.6.9 (talk) 13:20, 7 December 2010 (UTC)