  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.
