A modified generalized residual method for minimization problems with errors of a known level in weakened norms

An algorithm is proposed for the numerical solution of a quadratic minimization problem on an ellipsoid specified in the Hilbert space by a compact operator. This algorithm is a certain transform of the generalized residual method designed previously for the application in nonclassical information conditions when a priori information on the error level in an operator defining the cost functional is available only in the norms being weaker than the original ones. At the same time, the convergence of the algorithm is proved in the original norms. A number of simple numerical examples are discussed.