Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations

This paper presents a digest of recently developed simplicial and continuation methods for approximating fixed-points or zero-points of nonlinear finite-dimensional mappings. Underlying the methods are algorithms for following curves which are implicitly defined, as for example, in the case of homotopies. The details of several algorithms are outlined sufficiently that they should be easily implemented. Applications of simplicial and continuation methods to nonlinear complementarily, location of critical points, location of multiple solutions and bifurcation are presented.