Talk:Levenberg–Marquardt algorithm: Difference between revisions

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== L-M is for nonlinear least squares problems only ==

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:Both formulas have the same meaning, namely '''J'''^T'''Jq''' + λ'''q''' = −'''J'''^T'''f'''. As far as I am concerned, it is a matter of taste which you prefer, but the second is perhaps clearer. -- [[User:Jitse Niesen|Jitse Niesen]] ([[User talk:Jitse Niesen|talk]]) 20:46, 30 August 2005 (UTC)

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All formulas have a lack of negative sign. For example:

:<math>\mathbf{(J^{T}J)\boldsymbol \delta = J^{T} [y - f(\boldsymbol \beta)]} \!</math>

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finding this bug took quite some time. And it should be pointed out, how to get to this formula. --vogt31337 9:00 26 January 2012 (UTC) <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Vogt31337|Vogt31337]] ([[User talk:Vogt31337|talk]] • [[Special:Contributions/Vogt31337|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

@ Vogt31337:

i think there is no sign missing since '''J''' is the jacobian of '''f''' and '''f''' has a negativ sign in '''S'''. the goal is to minimize '''S''' and therefore we want to go in direction of negativ jacobian of

'''S''' which turns out to be the negative jacobian of '''-f''' and thus '''-(-J) = J'''. -- Georg

@ Vogt31337: I agree with you. -- D <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/192.55.54.42|192.55.54.42]] ([[User talk:192.55.54.42#top|talk]]) 23:13, 28 June 2019 (UTC)</small> <!--Autosigned by SineBot-->

==Transpose==

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In between the section Solution there is the sentence:

: >> Note that the gradient of ''S'' with respect to ''δ'' equals <math>-2(\mathbf{J}^{T} [\mathbf{y} - \mathbf{f}(\boldsymbol \beta) ] )^T </math> <<

: Is it not supposed to be: ... gradient of ''S'' with respect to '''&beta;''' ?? -Georg <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/31.18.248.89|31.18.248.89]] ([[User talk:31.18.248.89|talk]]) 20:45, 27 May 2014 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

== Notes and references==

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There should be discussion of the covariance of the solution. I think it's that if J is left-multiplied by the inverse of the input covariance, than <math>J^\top \Sigma^{-1} J</math> is the covariance of the output, or somesuch. [[User:BenFrantzDale|—Ben FrantzDale]] ([[User talk:BenFrantzDale|talk]]) 17:20, 26 October 2011 (UTC)

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