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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 4, Pages 578–586
(Mi zvmmf298)
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On the regularization of an equation of the first kind with a multiple integration operator
S. Yu. Sovetnikova, G. V. Khromova Saratov State University, ul. Astrakhanskaya 83, Saratov, 410026, Russia
Abstract:
The zero-order Tikhonov regularization method as applied to an equation of the first kind with a multiple differentiation operator is considered for the case when the solution belongs to a class from the domain of the adjoint operator. An estimate of the error of the approximate solution in the uniform metric is obtained, which is sharp with respect to the order, and the order is established. It is proved that the proposed method is optimal with respect to the order. Unimprovable estimates of the order of the modulus of continuity of the inverse operator are obtained.
Key words:
integral equation of the first kind, multiple integration operator, numerical regularization method, error bound.
Received: 17.10.2006
Citation:
S. Yu. Sovetnikova, G. V. Khromova, “On the regularization of an equation of the first kind with a multiple integration operator”, Zh. Vychisl. Mat. Mat. Fiz., 47:4 (2007), 578–586; Comput. Math. Math. Phys., 47:4 (2007), 555–563
Linking options:
https://www.mathnet.ru/eng/zvmmf298 https://www.mathnet.ru/eng/zvmmf/v47/i4/p578
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Abstract page: | 230 | Full-text PDF : | 115 | References: | 39 | First page: | 1 |
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