On simplex-based piecewise-linear approximations of non-linear mappings

Simplex-based piecewise-linear (PWL) approximations of non-linear mappings are needed when the robust PWL analysis is used to directly solve non-linear equations. This paper proposes a straightforward technique for transforming the well-known approximations into another form. This new form is computationally more efficient, since it preserves the sparse structure of the original Jacobian matrix. Furthermore, this new form of PWL approximation explicitly relates the simplex-based PWL analysis to the conventional formulation of the Katzenelson algorithm. The proposed transform technique is also extended to treat groupwise-separable mappings and, finally, non-separable but sparse mappings that arise in real-life simulation of large electronic circuits. In this paper, all these (transformed) simplex-based PWL approximations are compared in terms of their generality and efficiency. The computational efficiency of the PWL approximation that utilizes sparsity is validated with realistic simulations. Copyright (c) 2005 John Wiley & Sons, Ltd.