On the Gauss-Newton method for solving equations
We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved...
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Universidad Católica del Norte, Departamento de Matemáticas
2012
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oai:scielo:S0716-091720120001000022012-04-13On the Gauss-Newton method for solving equationsArgyros,Ioaniss KHitlout,Saïd Gauss-Newton method semilocal convergence Frechet- derivative Lipschitz/center-Lipschitz condition convergence domain We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solutioninfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.31 n.1 20122012-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100002en10.4067/S0716-09172012000100002 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Gauss-Newton method semilocal convergence Frechet- derivative Lipschitz/center-Lipschitz condition convergence domain |
| spellingShingle |
Gauss-Newton method semilocal convergence Frechet- derivative Lipschitz/center-Lipschitz condition convergence domain Argyros,Ioaniss K Hitlout,Saïd On the Gauss-Newton method for solving equations |
| description |
We use a combination of the center-Lipschitz condition with the Lipschitz condition condition on the Frechet-derivative of the operator involved to provide a semilocal convergence analysis of the Gauss-Newton method to a solution of an equation. Using more precise estimates on the distances involved, under weaker hypotheses, and under the same computational cost, we provide an analysis of the Gauss- Newton method with the following advantages over the corresponding results in [8]: larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location ofthe solution |
| author |
Argyros,Ioaniss K Hitlout,Saïd |
| author_facet |
Argyros,Ioaniss K Hitlout,Saïd |
| author_sort |
Argyros,Ioaniss K |
| title |
On the Gauss-Newton method for solving equations |
| title_short |
On the Gauss-Newton method for solving equations |
| title_full |
On the Gauss-Newton method for solving equations |
| title_fullStr |
On the Gauss-Newton method for solving equations |
| title_full_unstemmed |
On the Gauss-Newton method for solving equations |
| title_sort |
on the gauss-newton method for solving equations |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2012 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172012000100002 |
| work_keys_str_mv |
AT argyrosioanissk onthegaussnewtonmethodforsolvingequations AT hitloutsaid onthegaussnewtonmethodforsolvingequations |
| _version_ |
1718439780599988224 |