Is it possible to construct a sequence that converges in theory but when computed numerically with a computer program is diverging.
I feel that today our computer programs doesn't allow such pathological cases so I think I might found such pathological sequence working in simple precision.
Of course I want to avoid the case of overflows.
Finally, what would be an ill-conditioned sequence ? I have some examples about ode, matrix, ... but does there exist an ill-conditioned notion for sequences (defined by a recurrence relation) ?