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Adaptive cross approximation for ill-posed problems

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dc.contributor.author Mach, Thomas
dc.contributor.author Reichel, Lothar
dc.contributor.author Van Barel, Marc
dc.contributor.author Vandebril, R.
dc.date.accessioned 2017-01-06T09:32:09Z
dc.date.available 2017-01-06T09:32:09Z
dc.date.issued 2016-09-01
dc.identifier.citation Mach, T., Reichel, L., Van Barel, M., & Vandebril, R. (2016). Adaptive cross approximation for ill-posed problems. Journal of Computational and Applied Mathematics, 303, 206-217. DOI: 10.1016/j.cam.2016.02.020 ru_RU
dc.identifier.uri http://nur.nu.edu.kz/handle/123456789/2191
dc.description.abstract Integral equations of the first kind with a smooth kernel and perturbed right-hand side, which represents available contaminated data, arise in many applications. Discretization gives rise to linear systems of equations with a matrix whose singular values cluster at the origin. The solution of these systems of equations requires regularization, which has the effect that components in the computed solution connected to singular vectors associated with small singular values are damped or ignored. In order to compute a useful approximate solution typically approximations of only a fairly small number of the largest singular values and associated singular vectors of the matrix are required. The present paper explores the possibility of determining these approximate singular values and vectors by adaptive cross approximation. This approach is particularly useful when a fine discretization of the integral equation is required and the resulting linear system of equations is of large dimensions, because adaptive cross approximation makes it possible to compute only fairly few of the matrix entries. ru_RU
dc.language.iso en ru_RU
dc.publisher Journal of Computational and Applied Mathematics ru_RU
dc.rights Attribution-NonCommercial-ShareAlike 3.0 United States *
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/us/ *
dc.subject adaptive cross approximation ru_RU
dc.subject Ill-posed problem ru_RU
dc.subject inverse problem ru_RU
dc.subject regularization ru_RU
dc.subject sparse discretization ru_RU
dc.title Adaptive cross approximation for ill-posed problems ru_RU
dc.type Article ru_RU

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