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Mathematical Models and Computer Simulations

Erschienen in:

01.03.2019

Solution of the Fredholm Equation of the First Kind by the Mesh Method with the Tikhonov Regularization

verfasst von: A. A. Belov, N. N. Kalitkin

Erschienen in: Mathematical Models and Computer Simulations | Ausgabe 2/2019

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Abstract

We consider a linear ill-posed problem for the Fredholm equation of the first kind. For its regularization, Tikhonov’s stabilizer is implemented. To solve the problem, we use the mesh method, in which we replace integral operators by the simplest quadratures; and the differential ones, by the simplest finite differences. We investigate experimentally the influence of the regularization parameter and mesh thickening on the algorithm’s accuracy. The best performance is provided by the zeroth-order regularizer. We explain the reason of this result. We use the proposed algorithm for an applied problem of the recognition of two closely situated stars if the telescope instrument function is known. In addition, we show that the stars are clearly distinguished if the distance between them is ~0.2 of the instrumental function’s width and the values of brightness differ by 1–2 stellar magnitudes.

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Titel: Solution of the Fredholm Equation of the First Kind by the Mesh Method with the Tikhonov Regularization
verfasst von: A. A. Belov
N. N. Kalitkin
Publikationsdatum: 01.03.2019
Verlag: Pleiades Publishing
Erschienen in: Mathematical Models and Computer Simulations / Ausgabe 2/2019
Print ISSN: 2070-0482
Elektronische ISSN: 2070-0490
DOI: https://doi.org/10.1134/S2070048219020042

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