Computability
Do numerical orbits of chaotic dynamical processes represent true orbits?
Journal of Complexity
New computer methods for global optimization
New computer methods for global optimization
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Complexity theory of real functions
Complexity theory of real functions
Feasible real random access machines
Journal of Complexity
Computable analysis: an introduction
Computable analysis: an introduction
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
The iRRAM: Exact Arithmetic in C++
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
MPFR: A multiple-precision binary floating-point library with correct rounding
ACM Transactions on Mathematical Software (TOMS)
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The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. There are two main results. First, the computational complexity measure considered here is related to the Lyapunov exponent of the dynamical system under consideration. Second, the presented algorithm is optimal with regard to that complexity measure.