An iterated version of Lavrent’iev’s method for ill-posed equations with approximately specified data
Abstract
- An iterated version of the Lavrentiev’s method, in the setting of a Banach space, is suggested for obtaining stable approximate solutions for the ill-posed operator equation Au = v, when the data A and v are known only approximately. In the setting of a Hilbert space with appropriate a priori parameter choice, the suggested procedure yields order optimal error estimates. An iterated version of Tikhonov regularization yielding order optimal error estimate is a special case of the procedure. The assumption on the approximating operators show that the finite dimensional system arising out of it would be of smaller size for larger iterates. This aspect is compared with an assumption of [3] for a degenerate kernel method for integral equations of the first kind.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- CONTENTS
- Some problems of the theory of multidimensional inverse problems
- Complex force fields and complex orbits
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem
- An iterated version of Lavrent’iev’s method for ill-posed equations with approximately specified data
- Finding small inhomogeneities from scattering data
- An inverse problem for orthotropic medium
Articles in the same Issue
- CONTENTS
- Some problems of the theory of multidimensional inverse problems
- Complex force fields and complex orbits
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem
- An iterated version of Lavrent’iev’s method for ill-posed equations with approximately specified data
- Finding small inhomogeneities from scattering data
- An inverse problem for orthotropic medium
