Comments on "On the use of /spl rho/-algorithm in series acceleration"

Abstract

For original paper by Singh and Singh see IEEE Trans Antennas Propag., vol.39, p.1514-17, 1991 October. Tan comments that Singh and Singh have correctly stated that the /spl epsiv/ algorithm is effective for accelerating the convergence of alternating series whereas the /spl rho/ algorithm is suitable for monotonic series; Tan comments that they have failed to recognize that sequences containing the spatial- or spectral-domain Green's function series partial sums are not monotonic, but oscillatory about certain limiting values. In fact, this suggests that the /spl epsiv/ algorithm should be a more suitable accelerator for the spatial- or spectral-domain Green's function series. The use of an example of the monotonic series Sn=/spl Sigma//sub 1//sup n/1/(m/sup 2/) to illustrate the effectiveness of the /spl rho/ algorithm over the /spl epsiv/ algorithm is, therefore, not relevant in a paper whose objective concerns the study of effective accelerators for convergence of the spatial- or spectral-domain Green's function series.