On the Computation of Manifolds of Foldpoints for Parameter-Dependent Problems
R.X. Dai, Werner C. Rheinboldt · SIAM Journal on Numerical Analysis · 1990
For parameter-dependent nonlinear equations in $R^n $, a new augmentation method for computing submanifolds of foldpoints is presented. The underlying theory is based on a characterization, developed earlier, of foldpoints on solution manifolds of parameterized equations. The method allows for a locally convergent iterative computation of foldpoints of a certain class, for a continuation along paths of such foldpoints, and for a computation of simplicial approximations of higher-dimensional submanifolds of foldpoints of the same type.