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I am working on a 3D reconstruction system and I am looking to use a Levenberg-marquardt algorithm to do bundle adjustment. I am not too sure about how LM works and what it requires.

The model I am working with has multiple equations each with a number of parameters that are unknown and have to be found. The equations share a number of unknown parameters between them. I.e.

$ y_1 = u^2 + v^2 $

$ y_2 = u^2 + v^2 + k^2 $

where u, v and k are unknowns.

Am I correct in assuming that the first thing I should do is work out the Jacobian of the set of equations? Once I work out the Jacobian can I run that through the LM algorithm with the observed results to find out my parameters?

The equations work out a value that is a 2D coordinate. Do I have to split up the equations into $2$ separate $x$ and $y$ components and add them both as separate equations into the jacobian? or can I use the $(x,y)$ coordinate in a single equation?

Finally I realise that will be a lot of parameters that are not shared a lot of the equations, meaning that a lot of the first order derivatives will be $0$ values. Does that matter for LM?

Thanks in advance, hopefully this all makes sense.

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    I made this [tutorial article](http://www.imagingshop.com/articles/least-squares) about linear and nonlinear least-squares, including Levenberg-Marquardt method.2013-01-07

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