Geodesic
Approximation of finite-section equations by piecewise constant functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 731-745

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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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     author = {E. V. Lebedeva and S. G. Solodkii},
     title = {Approximation of finite-section equations by piecewise constant functions},
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E. V. Lebedeva; S. G. Solodkii. Approximation of finite-section equations by piecewise constant functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 731-745. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a0/