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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive