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Talk:Bernoulli numbers: Difference between revisions
→use of memoization: added a new section, corrected "reply" indentation from :: to :::.
(→Algorithm?: corrected a typo, added a couple of comments.) |
(→use of memoization: added a new section, corrected "reply" indentation from :: to :::.) |
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:: I just copied the Wikipedia algo. (with <strike>atribution</strike> attribution). People don't have to use it, but they don't have to search for at least one algo. --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 01:20, 12 March 2014 (UTC)
::: Yes, it sure ''looks'' simple. The programming solutions that used it also looks simple and clean. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 01:56, 12 March 2014 (UTC)
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The double sum formula used by the REXX example is #33 from the entry [http://mathworld.wolfram.com/BernoulliNumber.html Bernoulli number] on The Eric Weisstein's World of Mathematics (TM).
<br><br>
::::::: <math> B_n = \sum_{k=0}^n \frac{1}{k+1} \sum_{r=0}^k (-1)^r \binom kr r^n </math>
<br>
:::::::::::::: where <math> \binom kr</math> is a binomial coefficient.<br>
<br> -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 01:00, 18 March 2014 (UTC)
==use of memoization==
In the REXX programming solution, I added memoization for the COMB and PERM functions (combinations and permutations).
<pre>
For computing the Bernoulli numbers up to (and including):
50 values, memoization was 17% faster.
100 " " " 38% "
200 " " " 42% "
</pre>
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