Continuous regularization of linear operator equations in a Hilbert space

For the linear operator equation Au=f we offer a continuous regularization based on the stabilization of solutions of differential equations in a Hilbert space H. We assume that A is a positive operator and that the equation Au=f has a solution in H.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 503–510, November, 1968.