New tools for localization of limit cycles in recursive block floating point systems. (English) Zbl 0910.65053
Summary: Some important properties of recursive block floating point systems are derived. On their basis an algorithm for searching limit cycles in such systems is proposed. For any finite wordlength implementation of linear systems, an ellipsoidal set of initial conditions is found which generates all limit cycles in the system. It is applicable for any exhaustive search algorithm and also yields a sufficient condition for absence of limit cycles in (block) floating point systems.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A30 | Linear ordinary differential equations and systems |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
