An Algorithm for Piecewise-Linear Approximation of an Implicitly Defined Manifold

A simplicial method is used to approximate the solution manifold to a system of nonlinear equations, H(x) = θ, where H:RN + K → RN The method begins at a point x₀ in the solution set where the derivative DH(x₀ ) is of full rank. Given any ε > 0, a piecewise linear manifold is constructed along which \| H(x) \|_∞ < ε. An algorithm is presented to carry out this construction in an efficient fashion.