Cited By
View all- Renka R(2013)Nonlinear least squares and Sobolev gradientsApplied Numerical Mathematics10.1016/j.apnum.2012.12.00265(91-104)Online publication date: 1-Mar-2013
Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space
Pages 1242 - 1262
Abstract
The aim of this paper is to develop stepwise variable preconditioning for the iterative solution of monotone operator equations in Hilbert space and apply it to nonlinear elliptic problems. The paper is built up to reflect the common character of preconditioned simple iterations and quasi-Newton methods. The main feature of the results is that the preconditioners are chosen via spectral equivalence. The latter can be executed in the corresponding Sobolev space in the case of elliptic problems, which helps both the construction and convergence analysis of preconditioners. This is illustrated by an example of a preconditioner using suitable domain decomposition.
- Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space
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Society for Industrial and Applied Mathematics
United States
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Published: 01 April 2003
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Cited By
View all- Renka R(2013)Nonlinear least squares and Sobolev gradientsApplied Numerical Mathematics10.1016/j.apnum.2012.12.00265(91-104)Online publication date: 1-Mar-2013