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[WP34s] Regularized incomplete Beta function
05-05-2014, 08:30 PM
Post: #27
RE: [WP34s] Regularized incomplete Beta function
(05-05-2014 11:02 AM)Paul Dale Wrote:  Is it worthwhile using CNVG? 03 which will choose 1e-24 or 1e-32 for the convergence criteria (this command is more conservative in XROM than in user code)? This will mean an additional iteration but will give better result in DP mode.

If it really improves the result in DP mode and DP mode is available (i.e. on the 34s) it should be done - "accuracy is not optional". ;-) However, if the proposed routine runs in DP mode I could not find a case where the result had less than 30 correct digits.

Quote:I'd probably also increase the iteration limit to 6 or 7 to avoid the error case.

During my tests the result always converged within 3, sometimes 4 iterations. A possible fifth loop was added "just to be sure". The error message was essentially included for testing to get a feedback if something really goes wrong. It should never show up, and during my tests it never did.

Quote:I don't see why it would be worthwhile given the fast convergence of Halley's method. We'd only be getting at most a couple of extra digits in DP mode.

If (!) we can get some additional digits and (!) DP mode is available (34s) another iteration is fine by me. But honestly I do not think that this will happen. Do you have an example where a fifth iteration yields better accuracy?

FTR: for my own tests I used a threshold of 1E-8 for a SP result. I think 1E-14 is on the safe side, even in DP mode.

Dieter
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RE: [WP34s] Regularized incomplete Beta function - Dieter - 05-05-2014 08:30 PM



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