Development of simplex-based piecewise-linear approximations of nonlinear mappings

Simplex-based piecewise-linear approximations of nonlinear mappings are needed when piecewise-linear analysis is used to directly solve nonlinear equations. In this paper, a straightforward technique is proposed for transforming the well-known approximations into another form. This new form is computationally more efficient and, furthermore, it provides a direct mathematical link between the simplex-based piecewise-linear analysis and Katzenelson algorithm. The proposed transform technique is also utilized to reformulate, in a more systematic manner, a new general and efficient simplex-based approximation method.