Abstract
Up to this point we have always assumed that zero is a regular value of the smooth mapping H : RN+1 → RN. In the case that H represents a mapping arising from a discretization of an operator of the form ℌ : E1 × R → E2 where E1 and E2 represent appropriate Banach spaces, it is often of interest to approximate bifurcation points of the equation ℌ = 0. It is often possible to choose the discretization H in such a way that also the resulting discretized equation H = 0 has a corresponding bifurcation point. Under reasonable non-degeneracy assumptions it is possible to obtain error estimates for the bifurcation point of the original problem ℌ = 0. We shall not pursue such estimates here and refer the reader to the papers of Brezzi & Rappaz & Raviart and Beyn.
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© 1990 Springer-verlag Berlin Heidelberg
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Allower, E.L., Georg, K. (1990). Detection of Bifurcation Points Along a Curve. In: Numerical Continuation Methods. Springer Series in Computational Mathematics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61257-2_8
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DOI: https://doi.org/10.1007/978-3-642-61257-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64764-2
Online ISBN: 978-3-642-61257-2
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