Stable solution of a quadratic minimization problem with a nonuniformly perturbed operator by applying a regularized gradient method

A regularized gradient method is proposed for stable solution of a quadratic minimization problem under nonconventional information conditions when the error levels in a specified exact linear operator are known only in weakened norms. The convergence of the method with respect to the argument in the norm of the original space is proved. An example is given that explains in which situations the method can be applied.