The computation of simplicial approximations of implicitly defined p-dimensional manifolds

A method is presented for the computation of a simplicial approximation covering a subset M0 of a p-dimensional manifold M in Rn defined implicitly as the solution set of a nonlinear system F(x) = 0 of n−p equations in n unknowns, n > p ≥ 2. The subset M0 is either the intersection of M with some polyhedral domain in Rn and is assumed to be bounded and nonempty, or it is an entire manifold component which has no boundary, such as a sphere. The method represents a generalization of a simplicial approximation process for the case p = 2 developed earlier by the author and W. Rheinboldt.