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`