Great post! It may interest you that William Kahan has written quite extensively on the pitfalls of iterative algorithms on floating point numbers; his discuss

Great post! It may interest you that William Kahan has written quite extensively on the pitfalls of iterative algorithms on floating point numbers; his discussion of Muller's pathological recurrence on pp. 14+ of this paper seems particularly relevant. http://www.cs.berkeley.edu/~wkahan/Mindless.pdf http://www.cs.berkeley.edu/~wkahan/Mindless.pdf