  In this paper we present a convergence analysis for the Nystrom method
proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of
the combined boundary integral equation formulations of sound-soft acoustic
scattering problems in three-dimensional space. This fast and efficient scheme
combines FFT techniques and a polar change of variables that cancels out the
kernel singularity. We establish the stability of the algorithms in the $L^2$
norm and we derive convergence estimates in both the $L^2$ and $L^\infty$
norms. In particular, our analysis establishes theoretically the previously
observed super-algebraic convergence of the method in cases in which the
right-hand side is smooth.
