As extension of the Tadeusiewicz method for finding bounds on all solutions of piecewise-linear equations

Recently Tadeusiewicz proposed an interesting and efficient method for finding bounds of all solutions of piecewise-linear DC equations of transistor circuits. In this paper we extend the Tadeusiewicz method so as to include the cases where matrix diagonal elements are negative. We show explicit formulas and the conditions under which they call be applied. We also generalize it by introducing one additional parameter which corresponds to approximating the nonlinear function by a quadratic polynomial