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

TL;DR

This paper demonstrates that the Kozlov-Maz'ya iteration for elliptic boundary-value problems can be viewed as a Landweber iteration, leading to practical improvements like acceleration with conjugate gradients and better stopping criteria.

Contribution

It reveals the equivalence between Kozlov-Maz'ya and Landweber iterations and introduces enhancements for efficiency and practicality.

Findings

Kozlov-Maz'ya iteration is equivalent to Landweber iteration for the Laplacian.

Acceleration of the method using conjugate gradient algorithms.

Implementation of a more practical stopping criterion.

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.