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| lsfit and/or minlm guidance http://forum.alglib.net/viewtopic.php?f=2&t=4604 |
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| Author: | Sergey.Bochkanov [ Thu May 16, 2024 11:40 pm ] |
| Post subject: | Re: lsfit and/or minlm guidance |
Hi! Ideally, these algorithms should just work without any knowledge of the underlying math. The idea is that being a physicist is already good enough:) However, exponential fitting is extremely difficult. No, it is EXTREMELY difficult. In particular, its success sometimes depends on algorithm implementation in a non-obvious manner. Some design decision that greatly improve robustness in many important cases turn out to degrade performance in this case. The be specific, I am a bit concerned by the fact that ALGLIB way of regularizing steps may slow down convergence on convolved problems exactly like yours. I explain it in order for you to understand that there is a possibility that you did everything right, and that is ALGLIB that needs to get better. Now, several questions first: * did you fail to get past the first iteration when using analytic derivatives - or numerical gradient? * how many variables do you have? * sometimes exponential problems get easier when you solve them with tight box constraints first (to prevent accidental escape from the initial point), and then relax constraints and re-solve. Did you try something like that? And recommendations: * for your case (accurate computations over inaccurate experimental data) a small differentiation step is recommended. Something proportional to sqrt(machine_epsilon), like 1E-7 or 1E-6. But not less, you do not want rounding errors to amplify. * epsx can be chosen higher than the numerical differentiation step, like 1e-3 or 1e-4 for the beginning. |
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