TY  - JOUR
AB  - 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.
DA  - 1993
DO  - 10.1080/01630569308816536
KW  - Gauss-Newton method
KW  - foliations
KW  - parametrized equations
KW  - invariant manifolds
LA  - eng
IS  - 5-6
M2  - 503
PY  - 1993
SN  - 0163-0563
SP  - 503-514
T2  - Numerical Functional Analysis and Optimization
TI  - On smoothness and invariance properties of the gauss-newton method
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17842503
Y2  - 2024-11-22T04:04:47
ER  -