A continuous regularization method for a constrained pseudoinverse problem with additional restrictions on the input operators

Abstract

A two-parameter continuous regularization method is considered for a constrained pseudoinverse problem with input operators satisfying a generalized complementarity condition. The method is based on the stabilization of the solutions of differential equations in a Hilbert space. Convergence conditions refining those known previously are found. The main result is that the parameter functions are independent of each other. The stability of the method is established in the class of all possible constrained perturbations. A one-parameter continuous regularization method is studied for a special case of the problem with additional input operators.