Resumen
In this work we consider the semicirculant preconditioning of elliptic differential operators of the form Lu := - \epsilon \Delta u + au_x + bu_y + cu $$ in two cases: $0 < \epsilon \ll 1$ and $\epsilon \equiv 1$. The paper [Numer. Math., 81 (1998), pp. 211--249] provided extremely interesting and useful results in the first case. On the other hand, those appear to contradict basic results on preconditioning given in [SIAM J. Numer. Anal., 27 (1990), pp. 656--694]. We reobtain the results of [Numer. Math., 81 (1998), pp. 211--249] by a new approach which we believe to be more transparent. We also clarify the situation regarding the apparent contradiction with [SIAM J. Numer. Anal., 27 (1990), pp. 656--694]. Finally, we describe the distribution of the preconditioned eigenvalues in the uniformly elliptic case, $\epsilon \equiv 1$.