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May  2014, 8(2): 537-560. doi: 10.3934/ipi.2014.8.537

## Kozlov-Maz'ya iteration as a form of Landweber iteration

 1 Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99557-6660, United States

Received  July 2011 Revised  November 2012 Published  May 2014

We consider the alternating method of Kozlov and Maz'ya for solving the Cauchy problem for elliptic boundary-value problems. Considering the case of the Laplacian, we show that this method can be recast as a form of Landweber iteration. In addition to conceptual advantages, this observation leads to some practical improvements. We show how to accelerate Kozlov-Maz'ya iteration using the conjugate gradient algorithm, and we show how to modify the method to obtain a more practical stopping criterion.
Citation: David Maxwell. Kozlov-Maz'ya iteration as a form of Landweber iteration. Inverse Problems & Imaging, 2014, 8 (2) : 537-560. doi: 10.3934/ipi.2014.8.537
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