tmodel
Taylor Model Arithmetic for Rigorous Bound Propagation
Algorithm
Convergence Properties:
|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
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
Source
Header file: `ThirdParty/mc++/include/tmodel.hpp`