HP 50g Romberg Integration
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04-04-2014, 07:40 PM
Post: #13
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RE: HP 50g Romberg Integration
(04-04-2014 06:25 PM)peacecalc Wrote:Quote:but I've read the legacy algorithm is not the best one around (it's only there because it's been tried and tested since the HP-34C, the Saturn code since the HP-71B, I think). Yes, I tried successively 6, 8, 10 and noticed the exponential growth of the running times while the results would be improved only by a little. Without analyzing the code, this story soon crossed my mind :-) Wheat and chessboard problem (04-04-2014 06:25 PM)peacecalc Wrote: And your test function is a hard piece of cake because of its limits at 0 and 1, both are divergent. I'll try integrating it from 0 to 1/e then from 1/e to 1 and see if the results get better. In 1982 I wrote what was perhaps the shortest numerical integration program ever, using midpoint rectangles: it fit in 30 steps, on an algebraic calculator. Totally useless though, as only the few built-in functions could be integrated, to only a few decimal places: http://www.hpmuseum.org/cgi-sys/cgiwrap/...ead=216249 (Message #11) Regards, Gerson. |
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