Canonical piecewise-linear analysis

Any continuous resistive nonlinear circuit can be approximated to any desired accuracy by a global piecewise-linear equation in the canonical form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a + B x + \sum_{i=1}^{p}c_{i} |\langle \alpha_{i}, x \rangle - \beta_{i}|= 0</tex> . All conventional circuit analysis methods (nodal, mesh, cut set, loop, hybrid, modified nodal, tableau) are shown to always yield an equation of this form, provided the only nonlinear elements are two-terminal resistors and controlled sources, each modeled by a one-dimensional piecewise-linear function. The well-known Katzenelson algorithm when applied to this equation yields an efficient algorithm which requires only a minimal computer storage. In the important special case when the canonical equation has a lattice structure (which always occur in the hybrid analysis), the algorithm is further refined to achieve a dramatic reduction in computation time.