Tracing implicitly defined curves and the use of singular value decomposition

We consider tracing implicitly defined curves of parameter dependent nonlinear problems using predictor-corrector methods. Since singular value decomposition is most reliable when rank deficiency is involved, we will use it to detect the singular points. The relation between bifurcation points along the curves we are tracing and the singular value decomposition (SDV) will be established. This approach will be applied to regular, turning and bifurcation points. Numerical examples will be presented to give the details of the implementation and to show the efficiency of the method proposed.