An introduction to PL algorithms

We give a brief introduction to piecewise linear (PL) algorithms, also called complementary pivot or fixed point algorithms. Our approach is based on the fundamental presentation of Eaves [14], hence we describe the algorithms in the general setting of PL manifolds. In particular, we introduce the PL homotopy method of Eaves & Saigal [16]. The recently established class of variable dimension algorithms will be presented. We use a particular cone construction for handling the homotopy parameter. Special attention is given to convergence results. Numerical details of the algorithms can only be sketched. For a more detailed presentation of such algorithms and bibliographical remarks we refer to [4].