Comments, with reply, on "Adaptive algorithms with an automatic gain control feature" by T.J. Shan and T. Kailath

It is shown that the new LMS (least-mean-square) algorithm introduced in the above-titled paper (see ibid., vol.35, no.1, p.122-7, 1988) is not properly devised and that it may make the algorithm itself divergent or 'sleep' forever. The authors respond to three points raised by the commenters, noting that the first is the result of an error in the paper, and the second is a universal assumption for algorithms such as theirs and therefore they did not explicitly mention it. They agree that the commenter's third point is significant and means that the algorithm may tend not to work for high-dimensional vector X, but that a more definite statement will need accurate convergence analysis, which is not at hand.<
>