Approximation of finite-section equations by piecewise constant functions

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.