Yet this qualifies as a genuine method, since in principle you
could implement higher and higher precision floating-point systems
and achieve the desired accuracy by longer and longer runs with
this high-precision arithmetic. Of course this is impractical,
perhaps even ridiculous. There is also the problem of choosing
``good'' initial points---if we are lucky, the first initial point
we choose for whatever floating-point system we have will do the
trick---but there is no guarantee, and indeed the Lyapunov exponent
may converge to something totally different (or worse, something only
slightly different).