Levenberg Marquardt Reference

[assasincreed]

Hello everyone,

I have implemented the LMA succesfully in my thesis and calculated the necessary uncertanities using the method descrobe by Jim and Altenbach in another posts. Jim the DSP guy also showed using NIST standards that the multiplication of the final covariance matrix with the MSE provides good estimates of the standard deviations. I wanted to reference this in my thesis and was wondering if there is any report or published paper someone has done showing this.

Thanks,

[KHartley]

We do have a document on how ni uses them in our LabVIEW functions but I don't believe we have a report on it. It seems like you've found some good resources who understand the idea enough. It may be more beneficial to message them directly. This is all I could find on the topic that we publish and it is on the two methods we use. This may not be the best forum to post this in as this is mainly geared toward LabVIEW programming.

http://digital.ni.com/public.nsf/allkb/bacf6fdf1b40993686256cc300657ba4?OpenDocument

http://ae.natinst.com/public.nsf/webPreview/A73F4DA042356BBE862569F50053ABA1?OpenDocument

http://ae.natinst.com/public.nsf/webPreview/DCC01DFC8FC38C5686257118006D35F6?OpenDocument

Good luck on your thesis.

[altenbach · Accepted solution]

(Kyle, you last two links are broken.)

Chapter 15 of numerical recipes has some useful information.

[assasincreed]

Thank you very much Kyle, the two last links are broken as pointed by Altenbach.

Altenbach, I will go through Press et al again, thanks for the direction.

Altenbach, If there is any other discussion related to NI's LMA and error estimates I hope you wont mind a message from me directly to you :). 

regards,

[altenbach]

I am sure there are other disucssion, but since you did not give a link to the thread you are discussing, we don't have a reference to define "other". 😄

I think you were talking about this discussion. There is mention of Bevington's book, but I don't have a copy at hand at the moment. (I think there might be one in the lab).

[assasincreed]

Thanks Altenbach. Understood it well. The use of MSE is needed when the weighting used in the square of the differences during chi minimization is unknown. If they are assumed to be equal then weighting is not applied, hence NI's default values of 1 do not make any effect on the chi minimization (and is a smart default since it affects nothing). However to gather information on the confidence intervals, the covariance needs to be adjusted with MSE provided that the degrees of freedom are high. This is because the covariance matrix in this case is C = (Jt*J)^-1. Thought I'll share my understanding in case someone else looks for similar answers. A great reference also is the text by Menke, 1989. Geophysical Data Analysis: Discrete Inverse Theory. It covers these concepts very well.

regards,

[KHartley]

Sorry about that here is the fixed link. The last one was an edited version of the document but I didn't find any changes to it.  

http://digital.ni.com/public.nsf/allkb/A73F4DA042356BBE862569F50053ABA1

[altenbach]

That reference is for HiQ, not LabVIEW and also does not address the estimation of the error of the paramter estimates.

[altenbach]

Ultimately, I would like to collect all this in my Nonlinear Fitting community group. Your question is actually listed in the advanced topics of my charter document, but I did not get around writing something up yet.

It clearly needs to link and extended discussion of the above quoted discussion. One of these days......