Piecewise linear approximation of smooth compact fibers (Q700176)

For a twice differentiable map \(H:\mathbb R^n\mapsto\mathbb R^m\) the authors consider the \(n\)-dimensional compact and differentiable manifold \(F:=H^{-1}(y_0)\) for a point \(y_0\in\mathbb R^m\). An alternate approach for constructing the piecewise linear structure of the manifold \(F\) is developed. The complexity of the combinatorics is reduced greatly via an application of a well-behaved homotopy continuation method that has a simpler expense.