| HAL-Inria | Publications, software ... of Inria's scientists |
Conference papers
Time- and Space-Efficient Evaluation of Some Hypergeometric Constants
Abstract : The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$.
Cited literature [20 references]
https://hal.inria.fr/inria-00177850
Contributor : Emmanuel Thomé Connect in order to contact the contributor
Submitted on : Tuesday, October 9, 2007 - 2:04:48 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Sunday, April 11, 2010 - 10:34:15 PM
Contributor : Emmanuel Thomé Connect in order to contact the contributor
Submitted on : Tuesday, October 9, 2007 - 2:04:48 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM
Long-term archiving on: : Sunday, April 11, 2010 - 10:34:15 PM
File
zeta3.pdf
Publisher files allowed on an open archive