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It seems both names are used for the same algorithm:

least mean square - mainly literature before 1990, for example: Widrow, Bernard, and Samuel D. Stearns. "Adaptive signal processing prentice-hall." Englewood Cliffs, NJ (1985).

least mean squares - newer papers / popular posts, for example: wikipedia

What is the correct name? Does it matter? Is there a difference I miss?

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  • $\begingroup$ I always thought is was the former. Without plural. $\endgroup$ Jul 29, 2022 at 16:42

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According this 2005 Stanford reference, "Thinking about Thinking, the Discovery of the LMS Algorithm", in 1960 the algorithm was baptized least mean square.

I met Ted for the first time on a Friday afternoon in the fall of 1959. [...] We didn’t have a name for this algorithm. A year or so later, my Ph.D. students, James S. Koford, gave it the name LMS algorithm for “least mean square,” and the name stuck.

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