Adaptive cross approximation for ill-posed problems

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dc.contributor.authorMach, Thomas
dc.contributor.authorReichel, Lothar
dc.contributor.authorVan Barel, Marc
dc.contributor.authorVandebril, R.
dc.date.accessioned2017-01-06T09:32:09Z
dc.date.available2017-01-06T09:32:09Z
dc.date.issued2016-09-01
dc.description.abstractIntegral 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.identifier.citationMach, 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.2016.02.020ru_RU
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/2191
dc.language.isoenru_RU
dc.publisherJournal of Computational and Applied Mathematicsru_RU
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectadaptive cross approximationru_RU
dc.subjectIll-posed problemru_RU
dc.subjectinverse problemru_RU
dc.subjectregularizationru_RU
dc.subjectsparse discretizationru_RU
dc.titleAdaptive cross approximation for ill-posed problemsru_RU
dc.typeArticleru_RU

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