Geodesic
Modified two-step Levenberg-Marquardt methods in the hydraulic conductivity identification problem
Numerical methods and programming, Tome 14 (2013) no. 3, pp. 362-369.

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Some modifications of two-step Levenberg–Marquardt methods are proposed for the minimization of a residual function. The methods are used to numerically solve a model problem of hydraulic conductivity identification for a three-dimensional anisotropic confined aquifer. The efficiency of the modified two-step Levenberg-Marquardt methods is shown for the problems with and without errors in pressure measurements.
Keywords: minimization of residual functions; inverse problems. 
@article{VMP_2013_14_3_a11,
     author = {A. V. Elesin and A. Sh. Kadyrova},
     title = {Modified two-step {Levenberg-Marquardt} methods in the hydraulic conductivity identification problem},
     journal = {Numerical methods and programming},
     pages = {362--369},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_3_a11/}
}
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A. V. Elesin; A. Sh. Kadyrova. Modified two-step Levenberg-Marquardt methods in the hydraulic conductivity identification problem. Numerical methods and programming, Tome 14 (2013) no. 3, pp. 362-369. http://geodesic.mathdoc.fr/item/VMP_2013_14_3_a11/