On the acceleration of the convergence of certain iterative proceedings (I)
The research elaborated in this paper has its origin in the study of the convergence of the sequences generated through the use of certain methods derived from the well-known Newton-Kantorovich method for the simultaneous approximation of the solution of an equation in a linear normed space, and of...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2009-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/899 |
| _version_ | 1818474970815135744 |
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| author | Adrian Diaconu |
| author_facet | Adrian Diaconu |
| author_sort | Adrian Diaconu |
| collection | DOAJ |
| description | The research elaborated in this paper has its origin in the study of the convergence of the sequences generated through the use of certain methods derived from the well-known Newton-Kantorovich method for the simultaneous approximation of the solution of an equation in a linear normed space, and of the inverse of the Fréchet differential at this solution. An important place is given in the paper to the notion of convergence order of an approximant sequence of the solution of an equation. Considering given an approximant sequence which verifies certain conditions expressed through the inequalities (25), we will build another approximant sequence through the relations (22), with ameliorated convergence order. We will analyse certain special cases and, in the same time, we will determine optimal methods from the point of view of the convergence order. |
| first_indexed | 2024-04-14T04:43:13Z |
| format | Article |
| id | doaj.art-f15c7d1be1ee4ebda349c8150bfd4cf2 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-14T04:43:13Z |
| publishDate | 2009-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-f15c7d1be1ee4ebda349c8150bfd4cf22022-12-22T02:11:33ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2009-02-01381On the acceleration of the convergence of certain iterative proceedings (I)Adrian Diaconu0Babeş-Bolyai University, Cluj-NapocaThe research elaborated in this paper has its origin in the study of the convergence of the sequences generated through the use of certain methods derived from the well-known Newton-Kantorovich method for the simultaneous approximation of the solution of an equation in a linear normed space, and of the inverse of the Fréchet differential at this solution. An important place is given in the paper to the notion of convergence order of an approximant sequence of the solution of an equation. Considering given an approximant sequence which verifies certain conditions expressed through the inequalities (25), we will build another approximant sequence through the relations (22), with ameliorated convergence order. We will analyse certain special cases and, in the same time, we will determine optimal methods from the point of view of the convergence order.https://ictp.acad.ro/jnaat/journal/article/view/899convergence of the approximant sequences for operatorial equations in Banach spaces |
| spellingShingle | Adrian Diaconu On the acceleration of the convergence of certain iterative proceedings (I) Journal of Numerical Analysis and Approximation Theory convergence of the approximant sequences for operatorial equations in Banach spaces |
| title | On the acceleration of the convergence of certain iterative proceedings (I) |
| title_full | On the acceleration of the convergence of certain iterative proceedings (I) |
| title_fullStr | On the acceleration of the convergence of certain iterative proceedings (I) |
| title_full_unstemmed | On the acceleration of the convergence of certain iterative proceedings (I) |
| title_short | On the acceleration of the convergence of certain iterative proceedings (I) |
| title_sort | on the acceleration of the convergence of certain iterative proceedings i |
| topic | convergence of the approximant sequences for operatorial equations in Banach spaces |
| url | https://ictp.acad.ro/jnaat/journal/article/view/899 |
| work_keys_str_mv | AT adriandiaconu ontheaccelerationoftheconvergenceofcertainiterativeproceedingsi |