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Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
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F. Schöpfer
Published/Copyright:
February 4, 2009
Abstract
The Landweber method is a well-known iterative procedure to compute regularized solutions of linear operator equations in Hilbert spaces. Unfortunately it is also known to be very slow. Likewise its generalization to Banach spaces has good regularizing properties but slow convergence. This article intends to give a short survey about the use of sequential subspace optimization to accelerate this method while preserving its regularizing properties.
Key words.: sequential subspace optimization; regularization; Banach spaces; acceleration; Landweber method
Received: 2008-07-25
Published Online: 2009-02-04
Published in Print: 2009-February
© de Gruyter 2009
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- Recent results on the quasi-optimality principle
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- Regularization in Banach spaces — convergence rates by approximative source conditions
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- On the role of sparsity in inverse problems
- Optimal convergence rates for Tikhonov regularization in Besov scales
- An overview on convergence rates for Tikhonov regularization methods for non-linear operators
- Modulus of continuity and conditional stability for linear regularization schemes
- Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
Keywords for this article
sequential subspace optimization;
regularization;
Banach spaces;
acceleration;
Landweber method
Articles in the same Issue
- Minisymposium — Recent progress in regularization theory
- Recent results on the quasi-optimality principle
- An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space
- Regularization in Banach spaces — convergence rates by approximative source conditions
- On a parameter identification problem in linear elasticity
- Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
- On the role of sparsity in inverse problems
- Optimal convergence rates for Tikhonov regularization in Besov scales
- An overview on convergence rates for Tikhonov regularization methods for non-linear operators
- Modulus of continuity and conditional stability for linear regularization schemes
- Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
