Construction of a normal solution of non-linear ill-posed problems by the method of regularization

A new way of choosing the regularization parameter when solving an ill-posed problem with approximately specified non-linear operator is described, based on a comparison of the discrepancy with an auxiliary functional (principle of discrepancy comparison). With the aid of this principle, convergence of the regularized solution to the normal solution (in the absence of uniqueness) is obtained for a wide class of normed spaces. Efficient algorithms are given for finding the regularization parameter in practical computations.