Solution of a $2$-constrained pseudo-inversion problem by a relaxation method

A regularizing algorithm based on the solution of the Cauchy problem for a second-order linear differential equation in a Hilbert space is proposed for solving a $2$-constrained pseudo-inversion problem. Conditions are found for the stabilization of a solution of the Cauchy problem to a normal solution of this problem in the case of perturbed input data.