tea.mathoverflow.net - Discussion Feed (Am I allowed to do non-rigorous numerical analysis?)

Nilima comments on "Am I allowed to do non-rigorous numerical analysis?" (16627)

Nilima — Wed, 19 Oct 2011 14:41:47 -0700

My two-bits as a numerical analyst: it's entirely acceptable to state the computed 'a' is a numerical approximation to the desired 'a'. It's not OK in general to claim that the computed a is correct to 5 digits. In specific instances, one may assert: since the original problem has some features X, and we know numerical algorithms Y converge to the solution of the problem given X, the computed a is indeed a good approximation.

Without knowing more about the setting it's hard to provide more concrete advice. However, consider the following scenario: a is a global minimizer of a function with many local minima. There may be a numerical strategy which is based on computing the residual, and the computed a may indeed reduce the residual to 10^-5. That doesn't imply a is close to the computed a.

I'm sorry to be nit-picky.

quid comments on "Am I allowed to do non-rigorous numerical analysis?" (16621)

quid — Wed, 19 Oct 2011 06:51:35 -0700

This seems like a reasonable question to me; some more details might or might not be required but even in the current form it seems alright to me.

David Speyer comments on "Am I allowed to do non-rigorous numerical analysis?" (16620)

David Speyer — Wed, 19 Oct 2011 06:31:34 -0700

The question http://mathoverflow.net/questions/78576/am-i-allowed-to-do-non-rigorous-numerical-analysis has one close vote at the moment. I think it is interesting, although obviously subjective, and I'd be glad to hear from some experienced editors how they would treat this.

Basically, the question is the following. There is a real number a which plays an important role in the OP's paper. There is no closed formula for a, but he can approximate it numerically. If he publishes 5 digits of a, is that an implicit claim that he has rigorously proven a to lie in an interval of width 10^{-5}, or is it enough to have used numerical algorithms which are generally reliable?