On the discrepancy principle
نویسنده
چکیده
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy principle, in general, does not yield uniform with respect to the data convergence. An a priori choice of the regularization parameter is proposed and justified for some nonlinear operator equations.
منابع مشابه
A discrepancy principle for equations with monotone continuous operators
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter a(δ) is proved. Convergence of the solution obtained by the discrepancy principle is justified. The results are obtained under natural assumptions on the nonlinear operator. MSC: 47J05, 47J06, 47J35, 65R30
متن کاملNonlinear analysis: Theory, Methods and Applications, A discrepancy principle for equations with monotone continuous operators
A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter a(δ) is proved. Convergence of the solution obtained by the discrepancy principle is justified. The results are obtained under natural assumptions on the nonlinear operator. MSC: 47J05, 47J06, 47J35, 65R30
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