[WP34S] Speeding up the Romberg Integration Message #1 Posted by Les Wright on 29 May 2012, 5:12 a.m.
Just noticed in the SVN that the requirement for 3 diagonal elements of the Romberg matrix to agree to the desired accuracy has been dropped to two.
I believe that little is gained in most cases by doubling the running time of a problem (which is indeed what happens since the number of new function evaluations is the same as what one has already done when one moves to a new row), though I know one can argue that some integrands out there will converge spuriously to the wrong value and three element agreement will combat that. But for most problems, I think halving the running time is well worth it. My own port of the original PPC ROM IG routine requires only two elements to agree, and I usually use it in preference to the built in integrator.
On my wish list is the ability to control desired accuracy not through FIX n or, preferably, SCI n, but through an actual relative accuracy entered as one does on the 42S. This would enable one to aim for greater accuracy if desired than the ALL 00 or SCI 11 settings allow.
Just wanted to commend you on this wise refinement. It had crossed my mind once that it may be worth considering, but I never mentioned it.
Les
Edited: 29 May 2012, 5:13 a.m.
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