This package contains example problems for robustness testing of nonlinear algebraic equation solvers. It contains the following types of examples:

- Plain nonlinear algebraic equation systems: These can be solved using the well-known algorithms such as Newton-Raphson, Trust Region. See for instance all examples within AliasDifficult, Baharev2008, Baharev2009a, Baharev2009b, Lee2001.
- Nonlinear algebraic equation systems using probability-one homotopy maps: These are solved using continuation algorithms, and the construction of the homotopy maps use probability-one homotopy theory to guarantee convergence with probability one in sense of a Lebesgue measure. See for instance Melville1993, Roychowdhury2006.

This Modelica package is free software and the use is completely at your own risk; it can be redistributed and/or modified under the terms of the 3-Clause BSD License.

Name | Description |
---|---|

License | BSD 3-Clause License |

Melville1993 | R.C. Melville et al.: "Artificial Parameter Homotopy Methods for the DC Operating Point Problem", 1993. |

AliasDifficult | J.-P. Merlet et al.: "ALIAS difficult benches", 2007. |

Baharev2008 | A. Baharev, E. Rev: "Reliable Computation of Equilibrium Cascades with Affine Arithmetic", 2008. |

Baharev2009a | A. Baharev et al.: "Computation of an extractive distillation column with affine arithmetic", 2009. |

Baharev2009b | A. Baharev, E. Rev: "A complete nonlinear system solver using affine arithmetic", 2009. |

Lee2001 | T. Y. Lee, J. K. Shim: "Elimination-based solution method for the forward kinematics of the general Stewart-Gough platform", 2001. |

Roychowdhury2006 | J. Roychowdhury, R. Melville : "Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods", 2006. |

P1Homotopy | Probability-one homotopy utilities |

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