A FINITE DIMENSIONAL METHOD FOR SOLVING NONLINEAR ILL-POSED PROBLEMS

We propose a finite dimensional method to compute the solution of nonlin-ear ill-posed problems approximately and show that under certain conditions, theconvergence can be guaranteed. Moreover, we obtain the rate of convergence ofour method provided that the true solution satisfies suitable smoothness condition. Finally, we present two examples from the parameter estimation problems ofdifferential equations and illustrate the applicability of our method.