Geodesic
A regularized Levenberg--Marquardt type method applied to the structural inverse gravity problem in a multilayer medium and its parallel realization
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 3, pp. 5-15

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The structural inverse gravity problem in a multilayer medium is one of the most important geophysics problem. Until recently, the problem was reduced to the separation of gravitational fields and the restoration of unknown layers independently. Now the methods are in demand that allow find unknown layers simultaneously. For solving Urysohn integral equation of the first kind describing the problem regularized algorithms Levenberg–Marquardt type with weight factors are investigated. A new Levenberg–Marquardt type method based on Levenberg–Marquardt scheme is proposed. A regularized Levenberg–Marquardt type method compared with classic Levenberg-Marquardt method. For classic Levenberg–Marquardt method some computational optimizations are offered. The numerical experiments using model gravitational data allow to compare convergence rates, relative errors and program execution times of classic Levenberg–Marquardt algorithm and Levenberg–Marquardt method. The parallel programs implementing the algorithms are developed using CUDA and OpenMP technologies.
Keywords: Tikhonov regularization scheme, integral Urysohn type equation of first kind, regularized Levenberg–Marquardt method, regularized Levenberg–Marquardt type method, inverse gravimetry multilayer problem. 
@article{VYURV_2017_6_3_a0,
     author = {A. F. Skurydina},
     title = {A regularized {Levenberg--Marquardt} type method applied to the structural inverse gravity problem in a multilayer medium and its parallel realization},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {5--15},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2017_6_3_a0/}
}
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A. F. Skurydina. A regularized Levenberg--Marquardt type method applied to the structural inverse gravity problem in a multilayer medium and its parallel realization. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 3, pp. 5-15. http://geodesic.mathdoc.fr/item/VYURV_2017_6_3_a0/