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- Title
Improved local convergence analysis of the Gauss-Newton method under a majorant condition.
- Authors
Argyros, Ioannis; Magreñán, Á.
- Abstract
We present a local convergence analysis of Gauss-Newton method for solving nonlinear least square problems. Using more precise majorant conditions than in earlier studies such as Chen (Comput Optim Appl 40:97-118, ), Chen and Li (Appl Math Comput 170:686-705, ), Chen and Li (Appl Math Comput 324:1381-1394, ), Ferreira (J Comput Appl Math 235:1515-1522, ), Ferreira and Gonçalves (Comput Optim Appl 48:1-21, ), Ferreira and Gonçalves (J Complex 27(1):111-125, ), Li et al. (J Complex 26:268-295, ), Li et al. (Comput Optim Appl 47:1057-1067, ), Proinov (J Complex 25:38-62, ), Ewing, Gross, Martin (eds.) (The merging of disciplines: new directions in pure, applied and computational mathematics 185-196, ), Traup (Iterative methods for the solution of equations, ), Wang (J Numer Anal 20:123-134, ), we provide a larger radius of convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
- Subjects
GAUSS-Newton method; NONLINEAR analysis; LEAST squares; BANACH spaces; ITERATIVE methods (Mathematics); STOCHASTIC convergence
- Publication
Computational Optimization & Applications, 2015, Vol 60, Issue 2, p423
- ISSN
0926-6003
- Publication type
Article
- DOI
10.1007/s10589-014-9704-6