On the connection between the generalized discrepancy method and the generalized discrepancy principle for nonlinear ill-posed problems. (English. Russian original) Zbl 0547.65050
U.S.S.R. Comput. Math. Math. Phys. 22, No. 4, 13-22 (1982); translation from Zh. Vychisl. Mat. Mat. Fiz. 22, No. 4 783-790 (1982).
The generalized residual principle is a method for choosing the regularization parameter in Tikhonov’s method for the solution of ill- posed problems. It is shown that the approximations computed by this choice converge to the so-called normal solution of the problem. Then the method of the generalized residual for solving the ill-posed problem is stated. It is shown that under certain conditions the approximation from this method and the approximation from Tikhonov’s regularization method with the regularization parameter chosen by the generalized residual principle are identical.
Reviewer: H.Matthies
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 47J25 | Iterative procedures involving nonlinear operators |
