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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 5, Pages 731–745 (Mi zvmmf133)  
Approximation of finite-section equations by piecewise constant functions

E. V. Lebedeva, S. G. Solodkii

Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya ul. 3, Kiev, 01601, Ukraine
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Abstract: The problem is studied of reducing the amount of discrete information required for achieving a prescribed accuracy of solving Fredholm integral equations of the first kind on a half-line. The equations are solved by the finite-section method combined with piecewise constant interpolation of the kernel and the right-hand side at uniform grid points. The approximating properties of the discretization schemes are examined, and the corresponding computational costs are analyzed.
Key words: finite-section method, piecewise constant interpolation, ill-posed problem, Fredholm integral equation of the first kind.
Received: 21.12.2006
Revised: 12.11.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 5, Pages 693–706
DOI: https://doi.org/10.1134/S0965542508050011
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: E. V. Lebedeva, S. G. Solodkii, “Approximation of finite-section equations by piecewise constant functions”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008), 731–745; Comput. Math. Math. Phys., 48:5 (2008), 693–706
Citation in format AMSBIB
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