A note on the quadratic convergence of the inexact Newton methods
We show that a new sufficient condition for the convergence with \(q\)-order two of the inexact Newton iterates may be obtained by considering the normwise backward error of the approximate steps and a result on perturbed Newton methods. This condition is in fact equivalent to the characterization...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2000-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/662 |
| _version_ | 1828543259272544256 |
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| author | Emil Cătinaş |
| author_facet | Emil Cătinaş |
| author_sort | Emil Cătinaş |
| collection | DOAJ |
| description |
We show that a new sufficient condition for the convergence with \(q\)-order two of the inexact Newton iterates may be obtained by considering the normwise backward error of the approximate steps and a result on perturbed Newton methods.
This condition is in fact equivalent to the characterization given by Dembo, Eisenstat and Steihaug.
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| first_indexed | 2024-12-12T02:11:09Z |
| format | Article |
| id | doaj.art-83e8adf357314630a4596d441357c888 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-12T02:11:09Z |
| publishDate | 2000-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-83e8adf357314630a4596d441357c8882022-12-22T00:41:55ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2000-08-01292A note on the quadratic convergence of the inexact Newton methodsEmil Cătinaş0Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy We show that a new sufficient condition for the convergence with \(q\)-order two of the inexact Newton iterates may be obtained by considering the normwise backward error of the approximate steps and a result on perturbed Newton methods. This condition is in fact equivalent to the characterization given by Dembo, Eisenstat and Steihaug. https://www.ictp.acad.ro/jnaat/journal/article/view/662nonlinear systems of equations in \(R^n\)inexact Newton methodsinexact and perturbed Newton methodsconvergence ordersbackward errors |
| spellingShingle | Emil Cătinaş A note on the quadratic convergence of the inexact Newton methods Journal of Numerical Analysis and Approximation Theory nonlinear systems of equations in \(R^n\) inexact Newton methods inexact and perturbed Newton methods convergence orders backward errors |
| title | A note on the quadratic convergence of the inexact Newton methods |
| title_full | A note on the quadratic convergence of the inexact Newton methods |
| title_fullStr | A note on the quadratic convergence of the inexact Newton methods |
| title_full_unstemmed | A note on the quadratic convergence of the inexact Newton methods |
| title_short | A note on the quadratic convergence of the inexact Newton methods |
| title_sort | note on the quadratic convergence of the inexact newton methods |
| topic | nonlinear systems of equations in \(R^n\) inexact Newton methods inexact and perturbed Newton methods convergence orders backward errors |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/662 |
| work_keys_str_mv | AT emilcatinas anoteonthequadraticconvergenceoftheinexactnewtonmethods AT emilcatinas noteonthequadraticconvergenceoftheinexactnewtonmethods |