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). [an error occurred while processing this directive]
This method is clearly related to the Monte Carlo methods , with
the roundoff error associated with the floating-point arithmetic
playing the part of the random number generator required.