On smoothness and invariance properties of the gauss-newton method

Beyn W-J (1993)
Numerical Functional Analysis and Optimization 14(5-6): 503-514.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
OA
Abstract / Bemerkung
We consider systems of m nonlinear equations in m + p unknowns which have p-dimensional solution manifolds. It is well-known that the Gauss-Newton method converges locally and quadratically to regular points on this manifold. We investigate in detail the mapping which transfers the starting point to its limit on the manifold. This mapping is shown to be smooth of one order less than the given system. Moreover, we find that the Gauss-Newton method induces a foliation of the neighborhood of the manifold into smooth submanifolds. These submanifolds are of dimension m, they are invariant under the Gauss-Newton iteration, and they have orthogonal intersections with the solution manifold.
Stichworte
Gauss-Newton method; foliations; parametrized equations; invariant manifolds
Erscheinungsjahr
1993
Zeitschriftentitel
Numerical Functional Analysis and Optimization
Band
14
Ausgabe
5-6
Seite(n)
503-514
ISSN
0163-0563
eISSN
1532-2467
Page URI
https://pub.uni-bielefeld.de/record/1784250

Zitieren

Beyn W-J. On smoothness and invariance properties of the gauss-newton method. Numerical Functional Analysis and Optimization. 1993;14(5-6):503-514.
Beyn, W. - J. (1993). On smoothness and invariance properties of the gauss-newton method. Numerical Functional Analysis and Optimization, 14(5-6), 503-514. doi:10.1080/01630569308816536
Beyn, W. - J. (1993). On smoothness and invariance properties of the gauss-newton method. Numerical Functional Analysis and Optimization 14, 503-514.
Beyn, W.-J., 1993. On smoothness and invariance properties of the gauss-newton method. Numerical Functional Analysis and Optimization, 14(5-6), p 503-514.
W.-J. Beyn, “On smoothness and invariance properties of the gauss-newton method”, Numerical Functional Analysis and Optimization, vol. 14, 1993, pp. 503-514.
Beyn, W.-J.: On smoothness and invariance properties of the gauss-newton method. Numerical Functional Analysis and Optimization. 14, 503-514 (1993).
Beyn, Wolf-Jürgen. “On smoothness and invariance properties of the gauss-newton method”. Numerical Functional Analysis and Optimization 14.5-6 (1993): 503-514.
Alle Dateien verfügbar unter der/den folgenden Lizenz(en):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Volltext(e)
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-06T08:48:54Z
MD5 Prüfsumme
da0e2bb55f0b773772cdb247ed09da33