packageAlgebraTestSuite

Information

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.

Contents

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