Abstract
In the introduction some contexts were described in which underdetermined systems of nonlinear equations H(x, λ) = 0 arose. We saw that in general, such a system implicitly defines a curve or one-manifold of solution points. The theme of this book is to describe methods for numerically tracing such curves. In this chapter, we begin by describing some basic ideas. To make the context of our discussion precise, let us make the following
(2.1.1) Assumption. H : RN+1→ RN is a smooth map.
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© 1990 Springer-Verlag Berlin Heidelberg
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Allgower, E.L., Georg, K. (1990). The Basic Principles of Continuation Methods. In: Numerical Continuation Methods. Springer Series in Computational Mathematics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61257-2_2
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DOI: https://doi.org/10.1007/978-3-642-61257-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64764-2
Online ISBN: 978-3-642-61257-2
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