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- R Plato, U Hh Amarik Zz
- 2007

We consider generalized inverses and linear ill-posed problems in Banach spaces, and the concept of pseudo-optimal parameter choices and stopping rules for regularization methods is presented. The pseudo-optimality of the discrepancy principle for iterative methods like the Richardson iteration is shown, as well as the pseudo-optimality of diierent… (More)

- I Wallstabe, R Plato, A Weimann
- Endoscopy
- 2010

- R. PLATO
- 2007

In this paper resolvent estimates for Abel integral operators are provided. These estimates are applied to deduce regularizing properties of Lavrentiev's m-times iterated method as well as iterative schemes ? with the discrepancy principle as corresponding parameter choice or stopping rule, respectively for solving the corresponding Abel integral equations… (More)

- Robert Plato
- Adv. Comput. Math.
- 2012

- Robert Plato
- 2007

- R. PLATO
- 2007

For the numerical solution of the Galerkin equations associated with linear ill-posed problems that are symmetric and positive semideenite, the method of conjugate residuals is considered. An a posteriori stopping rule is introduced, and associated estimates for the approximations are provided which are order-optimal with respect to noise in the right-hand… (More)

- Robert Plato
- Numerical Algorithms
- 1999

We consider an ill-posed problem Ta = f* in Hilbert spaces and suppose that the linear bounded operator T is approximately available, with a known estimate for the operator perturbation at the solution. As a numerical scheme the CGNR-method is considered, that is, the classical method of conjugate gradients by Hestenes and Stiefel applied to the associated… (More)

- Robert Plato
- 2010

The repeated trapezoidal method was considered by P. Eggermont for the numerical solution of weakly singular Volterra integral equations of the first kind with exactly given right-hand sides ([7]). In the present paper we consider the regularizing properties of this method for perturbed right-hand sides. Finally, numerical results are presented.

- Robert Plato
- Comput. Meth. in Appl. Math.
- 2017

- Robert Plato
- 2007

We consider an ill-posed problem T u = f in Hilbert spaces and suppose that the linear bounded operator T is approximately available, with a known estimate for the operator perturbation at the solution. As a numerical scheme the CGNRRmethod is considered, this is, the method of conjugate gradients for solving the associated normal equations. Two a… (More)