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Computation of cusp singularities for operator equations and their discretizations

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Book cover Continuation Techniques and Bifurcation Problems

Abstract

We discuss the direct calculation of cusp singularities as solutions of a minimally augmented defining system, which is nonsingular under the canonical cusp conditions. The underlying operator equation may have any finite Fredholm index, and bounds on the discretization error are derived for the case of projection methods.

This work was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.

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Author information

Authors and Affiliations

  1. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439-4801, USA

    Andreas Griewank

  2. Mathematics Department, Southern Methodist University, Dallas, TX, 75275, USA

    George W. Reddien

Authors
  1. Andreas Griewank
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  2. George W. Reddien
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Arizona State University, Tempe, Arizona, 85287-1804, USA

    Hans D. Mittelmann

  2. Department Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan 200 A, B-3030, Leuven, Belgium

    Dirk Roose

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© 1990 Springer Basel AG

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Griewank, A., Reddien, G.W. (1990). Computation of cusp singularities for operator equations and their discretizations. In: Mittelmann, H.D., Roose, D. (eds) Continuation Techniques and Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 92. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5681-2_9

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  • DOI: https://doi.org/10.1007/978-3-0348-5681-2_9

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-2397-4

  • Online ISBN: 978-3-0348-5681-2

  • eBook Packages: Springer Book Archive

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