  Lavrent'ev regularization for the autoconvolution equation was considered by
J. Janno in {\itshape Lavrent'ev regularization of ill-posed problems
containing nonlinear near-to-monotone operators with application to
autoconvolution equation}, Inverse Problems, 16(2):333--348, 2000. Here this
study is extended by considering discretization of the Lavrent'ev scheme by
splines. It is shown how to maintain the known convergence rate by an
appropriate choice of spline spaces and a proper choice of the discretization
level. For piece-wise constant splines the discretized equation allows for an
explicit solver, in contrast to using higher order splines. This is used to
design a fast implementation by means of post-smoothing, which provides
results, which are indistinguishable from results obtained by direct
discretization using cubic splines.
