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Large sparse continuation problems

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Continuation Techniques and Bifurcation Problems

Abstract

We study and develop efficient and versatile Predictor-Corrector continuation methods for large sparse problems. The first object is to show how special solving methods for a large sparse linear systems can be incorporated into the basic steps of a continuation method. Next we describe how to use a special nonlinear conjugate gradient method to perform the corrector phase. It is shown how such methods can be used to detect bifurcation points, and how to trace bifurcating solution branches by using local perturbations. Finally, a numerical example involving bifurcating branches of a nonlinear eigenvalue problem is given.

Partially supported by UNI-ONR N0014-86K0687.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    E. L. Allgower & K. Georg

  2. Department of Applied Mathematics, National Chung-Hsing University, Taichung, 400, Taiwan, R.O.C.

    C.-S. Chien

  3. Institute of Applied Mathematics, University of Bonn, D-5300, Bonn 1, Fed. Rep. Germany

    K. Georg

Authors
  1. E. L. Allgower
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  2. C.-S. Chien
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  3. K. Georg
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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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Allgower, E.L., Chien, CS., Georg, K. (1990). Large sparse continuation problems. 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_1

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  • DOI: https://doi.org/10.1007/978-3-0348-5681-2_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-2397-4

  • Online ISBN: 978-3-0348-5681-2

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