A Refined Gauss-Newton- Mysovskii Theorem.
Please always quote using this URN: urn:nbn:de:0297-zib-541
- The present paper contains a generalization of a refinement of the Newton- Mysovskii theorem, recently obtained by the authors, to the case of Gauss-Newton procedures for solving nonlinear least-squares problems with full Jacobians. Invariant sufficient conditions are given that ensure the convergence of the Gauss-Newton iterates towards a solution of the problem, as well as the uniqueness of that solution in an explicitely defined neighborhood. It is shown by a counter- example that the results do not carry over to the rank deficient case.
| Author: | Peter Deuflhard, Florian Potra |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1991/07/18 |
| Series (Serial Number): | ZIB-Report (SC-91-04) |
| ZIB-Reportnumber: | SC-91-04 |
| Published in: | cf. P. Deuflhard, A. Hohmann: Numerische Mathematik I, 2nd rev. ed., de Gruyter, Berlin, New York 1993, chapter 4 |
