If one is interested in software development methodology, I strongly recommend taking 15 minutes to read the actual "waterfall" paper[1].
Poor guy, Winston Royce is one of the most misunderstood folks in the industry.
(By the way, curiously enough, Royce's son William was a major contributor to the Rational Unified Process.)
[1] http://www.cs.umd.edu/class/spring2003/cmsc838p/Process/wate...
The graphic where he shows cycles going back stages is used to exemplify failure, which he proposes to fix via the strict practices above.
Just in case someone from the future misunderstands this: I don't mean that agile drops analysis, documentation, planning or monitoring (they are essential to it) but it leaves the "intensive" and "before" parts out.