Convergence Properties
Mathematical Formulation
|R| = O(diam(D)^{q+1}) as domain shrinks Higher order q → faster convergence but more coefficients Used in global optimization branch-and-bound for bound tightening.
Complexity
Bernstein conversion: O(n^q * 2^n) but provides hull property
Implementations
SHOT
- tmodel.hpp - Taylor Model Arithmetic for Rigorous Bound Propagation
References
- Makino & Berz (2003) - Taylor models and validated numerics
- Neumaier (2002) - Taylor forms for global optimization
- Lin & Rokne (1995) - Bernstein form for polynomial bounds
- Sahlodin & Chachuat (2011) - McCormick-Taylor models
- Bompadre et al. (2012) - Convergence of Taylor models