Approximation of finite-section equations by piecewise constant functions |
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Authors: | E. V. Lebedeva S. G. Solodky |
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Affiliation: | (1) 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. |
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Keywords: | finite-section method piecewise constant interpolation ill-posed problem Fredholm integral equation of the first kind |
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