Geodesic
A discrete algorithm for the localization of lines of discontinuity of a~two-variable function
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 3-12

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We consider an ill-posed problem for the localization of lines of discontinuity. It is assumed that, instead of the exact function $f$, we know the values at the points of the uniform grid of the mean squares of the disturbed function $f^\delta$, $\|f-f^\delta\|_{L_2(\mathbb R^2)}\le\delta$, and the level of the error $\delta$. We construct an algorithm for the localization of lines of discontinuity, prove its convergence with approximation accuracy estimates whose order coincides with that of the estimates obtained earlier by the authors for the case when the function itself is given instead of the mean values of $f^\delta$. We also justify estimates for an important characteristic of the algorithm, separability threshold.
Keywords: ill-posed problem, regularization method, line of discontinuity, discretization, separability threshold. 
@article{SJIM_2017_20_4_a0,
     author = {A. L. Ageev and T. V. Antonova},
     title = {A discrete algorithm for the localization of lines of discontinuity of a~two-variable function},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {3--12},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a0/}
}
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A. L. Ageev; T. V. Antonova. A discrete algorithm for the localization of lines of discontinuity of a~two-variable function. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 3-12. http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a0/