HP 50g Romberg Integration

[Gerson W. Barbosa]

(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).

That maybe is true, but it is not fair, because when you use the Romberg method with the iteration depth of 20, the program have to calculate 2^20 - 1 function values, this are at least over a million, no wonder about the time you have to wait...
I don't know wether a side effect occures: so many additions can cause a summation error???

Did you try the lower iteration depths and how the results behavier is?

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.