Projected Newton method for a system of Tikhonov-Morozov equations

In this paper we derive a Newton type method to solve the non-linear system formed by combining the Tikhonov normal equations and Morozov's discrepancy principle. We prove that by placing a bound on the step size of the Newton iterations the method will always converge to the solution. By projecting the problem onto a low dimensional Krylov subspace and using the method to solve the projected non-linear system we show that we can reduce the computational cost of the method.