Summary
In this paper we consider the numerical location of generalized turning points by forming local model functions which reflect the rank drop characteristics of the original problem. As it turns out the resulting iterative procedure is equivalent to solving a certain augmented nonlinear system recently introduced by A. Griewank and G. W. Reddien [6–8]. After discussing various ways of obtaining the required second derivative information the paper concludes with some numerical experiments in Computing a simple bifurcation point of a two point boundary value problem.
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Griewank, A. (1984). Quadratically Appended Linear Models for Locating Generalized Turning Points. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_11
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_11
Publisher Name: Birkhäuser, Basel
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