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.<>