Zur regularisierten Lösung einer nichtlinearen nichtkorrekten Faltungsgleichung. (German) Zbl 0573.65110
Wiss. Z., Pädagog. Hochsch. ”Liselotte Herrmann” Güstrow, Math.- Naturwiss. Fak. 20, 163-178 (1982).
Considering the nonlinear ill-posed convolution equation \(x*x=b\) in the Banach space C[0,1] a uniqueness theorem will be proved. For the stable approximation of the solution a regularization method is constructed analytically and realized numerically. Precision of results and numerical effects are demonstrated by means of an example from statistics.