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

David Maxwell

doi:10.3934/ipi.2014.8.537

Article Contents

2014, Volume 8, Issue 2: 537-560. Doi: 10.3934/ipi.2014.8.537

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

David Maxwell^1,

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

Received: June 30, 2011

Revised: October 31, 2012

Published: April 2014

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Abstract

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.

Keywords:

Elliptic Cauchy problem,
iterative methods.

Mathematics Subject Classification: Primary: 35R30; Secondary: 65N21.

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