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Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method
-
A. B. Bakushinskii
and
M.Yu. Kokurin
Published/Copyright:
September 7, 2013
Abstract
- We present a class of iterative methods for solving nonlinear ill-posed operator equations with differentiable operators in a Banach space. The methods are based on regularization of the linearized equation by using an appropriate regularization scheme at each iteration. We establish that the iterations converge locally with power rate provided that the solution admits of a sourcewise representation. We also prove that the condition of sourcewise representability is very close to a necessary condition for this kind of estimates.
Published Online: 2013-09-07
Published in Print: 2001-08
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Contents
- Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
- On local solvability of inverse dissipative scattering problems
- Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method
- Iterative methods for an inverse heat conduction problem
- Identification of a special class of memory kernels in one-dimensional heat flow
- Nonlinear inverse problems for elliptic equations
- Inverse problem for interior spectral data of the Sturm – Liouville operator
Articles in the same Issue
- Contents
- Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
- On local solvability of inverse dissipative scattering problems
- Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method
- Iterative methods for an inverse heat conduction problem
- Identification of a special class of memory kernels in one-dimensional heat flow
- Nonlinear inverse problems for elliptic equations
- Inverse problem for interior spectral data of the Sturm – Liouville operator
