Geodesic
Regularized inversion of full tensor magnetic gradient data
Numerical methods and programming, Tome 17 (2016) no. 1, pp. 13-20

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Features of numerical solution of the three-dimensional ill-posed problem devoted to the inversion of full tensor magnetic gradient data are considered. This problem is simulated by a system of two three-dimensional Fredholm integral equations of the first kind. The Tikhonov regularization is applied to solve this ill-posed problem. The conjugate gradient method is used as a minimization method. The choice of the regularization parameter is realized according to the generalized residual principle with consideration of round-off errors capable of affecting the final result of calculations significantly.
Keywords: magnetostatics, full tensor magnetic gradient data, inverse problems, ill-posed problems, regularization method. 
@article{VMP_2016_17_1_a2,
     author = {Y. Wang and D. V. Luk'yanenko and A. G. Yagola},
     title = {Regularized inversion of full tensor magnetic gradient data},
     journal = {Numerical methods and programming},
     pages = {13--20},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a2/}
}
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Y. Wang; D. V. Luk'yanenko; A. G. Yagola. Regularized inversion of full tensor magnetic gradient data. Numerical methods and programming, Tome 17 (2016) no. 1, pp. 13-20. http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a2/