A Generalized Tikhonov Regularization and A-Priori Choice of Regularization Parameters

With aid of the regularizing filters, a new class of regularization methods which called generalized Tikhonov regularization for solving the first kind equations with perturbed operators and noisy data is constructed. Applying singular systems of compact operators, the convergence and optimum asymptotic order of the regularized solution is obtained by a-priori choosing regularization parameters.