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Numerische Mathematik

, Volume 34, Issue 4, pp 439–455 | Cite as

Strong uniqueness and second order convergence in nonlinear discrete approximation

  • Krisorn Jittorntrum
  • M. R. Osborne
Article

Summary

Strong uniqueness has proved to be an important condition in demonstrating the second order convergence of the generalised Gauss-Newton method for discrete nonlinear approximation problems [4]. Here we compare strong uniqueness with the multiplier condition which has also been used for this purpose. We describe strong uniqueness in terms of the local geometry of the unit ball and properties of the problem functions at the minimum point. When the norm is polyhedral we are able to give necessary and sufficient conditions for the second order convergence of the generalised Gauss-Newton algorithm.

Subject Classifications

AMS(MOS): 65D15 CR: 5.13 

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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Krisorn Jittorntrum
    • 1
  • M. R. Osborne
    • 2
  1. 1.Mathematics DepartmentChieng mai UniversityChieng maiThailand
  2. 2.Department of Statistics, Research School of Social SciencesAustralian National UniversityCanberraAustralia

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