ON SMOOTHNESS AND INVARIANCE PROPERTIES OF THE GAUSS-NEWTON METHOD

被引:1
作者
BEYN, WJ [1 ]
机构
[1] UNIV BIELEFELD,FAK MATH,D-33501 BIELEFELD,GERMANY
关键词
GAUSS-NEWTON METHOD; PARAMETRIZED EQUATIONS; INVARIANT MANIFOLDS; FOLIATIONS;
D O I
10.1080/01630569308816536
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
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页码:503 / 514
页数:12
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