Efficient Numerical Pathfollowing Beyond Critical Points

The paper presents a numerical pathfollowing technique based on an implicit change of parametrization using QR-decomposition. An automatic steplength control for tangent continuation is derived on a theoretical basis. In the suggested approach, turning points do not play any exceptional role. For the actual computation of (simple) bifurcation points, a special algorithm based on the augmented system of Moore is developed. This treatment includes imperfect bifurcations and permits an easy way of branch switching. An efficient linear equation solver is worked out in connection with the QR-decomposition. Finally, numerical comparisons are included that clearly document the efficiency of the newly developed algorithms.