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How does Mathematica perform numerical calculations?

Posted 10 years ago
POSTED BY: Luther Nayhm
5 Replies

I suspect the jumps are artifacts of error estimates deciding either to refine or not.

POSTED BY: Daniel Lichtblau

What I wrote here probably has something to offer in the way of explaining jumps involving error estimates. In brief, a refinement might or might not be made depending on which side of a test you are on (just passing, or just failing), and that can give rise to a jump.

Also, as noted in another response, absent a concrete example it is nearly impossible to speculate (and that applies to more than one question today).

POSTED BY: Daniel Lichtblau
Posted 10 years ago

Yes, thanks. It does, but it opened up another set of questions. The issue was not just the smooth curve, it was what the higher precision and accuracy curves were, what they mean if anything and whether they are telling me things that the smooth curve was not. This point is a bit clearer in the attachment above in the last figure of the set of four.

I would have replied to the previous post you commented on, but that thread was closed for "drifting" off topic. Thanks for getting back on this.

POSTED BY: Luther Nayhm

I suggest you post the calculation you're doing. It's easier to help with a specific question than a very general one.

POSTED BY: Frank Kampas
Posted 10 years ago

Yes, for sure. The attached worksheet also contains a dialog as to what I am trying to accomplish and what my questions are relating to the plots I am generating.

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POSTED BY: Luther Nayhm
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