Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement
Let f: B(x_0, R) \subset X \to Y be an operator from a closed ball of a Banach space X to a Banach space Y . We give new conditions to ensure the convergence of Newton-Kantorovich approximations toward a solution of the equation f(x) = 0 , under the hypothesis that f' be Hölder continuous. The...
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| Veröffentlicht in: | Zeitschrift für Analysis und ihre Anwendungen 1998-01, Vol.17 (2), p.271-280 |
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| Sprache: | eng |
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| container_end_page | 280 |
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| container_issue | 2 |
| container_start_page | 271 |
| container_title | Zeitschrift für Analysis und ihre Anwendungen |
| container_volume | 17 |
| creator | De Pascale, Espedito Zabreiko, Petr P. |
| description | Let
f: B(x_0, R) \subset X \to Y
be an operator from a closed ball of a Banach space
X
to a Banach space
Y
. We give new conditions to ensure the convergence of Newton-Kantorovich approximations toward a solution of the equation
f(x) = 0
, under the hypothesis that
f'
be Hölder continuous. The case of
f'
being Hölder continuous in a generalized sense is analyzed as well. |
| doi_str_mv | 10.4171/zaa/821 |
| format | Article |
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f: B(x_0, R) \subset X \to Y
be an operator from a closed ball of a Banach space
X
to a Banach space
Y
. We give new conditions to ensure the convergence of Newton-Kantorovich approximations toward a solution of the equation
f(x) = 0
, under the hypothesis that
f'
be Hölder continuous. The case of
f'
being Hölder continuous in a generalized sense is analyzed as well.</description><identifier>ISSN: 0232-2064</identifier><identifier>EISSN: 1661-4534</identifier><identifier>DOI: 10.4171/zaa/821</identifier><language>eng</language><ispartof>Zeitschrift für Analysis und ihre Anwendungen, 1998-01, Vol.17 (2), p.271-280</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c256t-4e22c103e562f097148e8c3b649f69ee314570b574fb887ea5fefb2fe19bcbb33</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>De Pascale, Espedito</creatorcontrib><creatorcontrib>Zabreiko, Petr P.</creatorcontrib><title>Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement</title><title>Zeitschrift für Analysis und ihre Anwendungen</title><description>Let
f: B(x_0, R) \subset X \to Y
be an operator from a closed ball of a Banach space
X
to a Banach space
Y
. We give new conditions to ensure the convergence of Newton-Kantorovich approximations toward a solution of the equation
f(x) = 0
, under the hypothesis that
f'
be Hölder continuous. The case of
f'
being Hölder continuous in a generalized sense is analyzed as well.</description><issn>0232-2064</issn><issn>1661-4534</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><recordid>eNotkMtKxDAYRoMoWMbBV8jOVZ3c07qT4mVw1I0KrkqS_pkWbDKkcUSf3g66-vgW5ywOQueUXAqq6erHmFXF6BEqqFK0FJKLY1QQxlnJiBKnaDlNg50_V0xTVqD3JoY9pC0EBzh6nHvAT_CVYygfTMgxxf3gevwIuY8d_gwdJPwGKW9hGPHMdkMeYpiusDlgeD3uZgJGCPkMnXjzMcHyfxfo9fbmpbkvN8936-Z6UzomVS4FMOYo4SAV86TWVFRQOW6VqL2qATgVUhMrtfC2qjQY6cFb5oHW1lnL-QJd_HlditOUwLe7NIwmfbeUtIco7RylnaPwX4dQVZs</recordid><startdate>19980101</startdate><enddate>19980101</enddate><creator>De Pascale, Espedito</creator><creator>Zabreiko, Petr P.</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19980101</creationdate><title>Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement</title><author>De Pascale, Espedito ; Zabreiko, Petr P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c256t-4e22c103e562f097148e8c3b649f69ee314570b574fb887ea5fefb2fe19bcbb33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>De Pascale, Espedito</creatorcontrib><creatorcontrib>Zabreiko, Petr P.</creatorcontrib><collection>CrossRef</collection><jtitle>Zeitschrift für Analysis und ihre Anwendungen</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>De Pascale, Espedito</au><au>Zabreiko, Petr P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement</atitle><jtitle>Zeitschrift für Analysis und ihre Anwendungen</jtitle><date>1998-01-01</date><risdate>1998</risdate><volume>17</volume><issue>2</issue><spage>271</spage><epage>280</epage><pages>271-280</pages><issn>0232-2064</issn><eissn>1661-4534</eissn><abstract>Let
f: B(x_0, R) \subset X \to Y
be an operator from a closed ball of a Banach space
X
to a Banach space
Y
. We give new conditions to ensure the convergence of Newton-Kantorovich approximations toward a solution of the equation
f(x) = 0
, under the hypothesis that
f'
be Hölder continuous. The case of
f'
being Hölder continuous in a generalized sense is analyzed as well.</abstract><doi>10.4171/zaa/821</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0232-2064 |
| ispartof | Zeitschrift für Analysis und ihre Anwendungen, 1998-01, Vol.17 (2), p.271-280 |
| issn | 0232-2064 1661-4534 |
| language | eng |
| recordid | cdi_crossref_primary_10_4171_zaa_821 |
| source | European Mathematical Society Publishing House |
| title | Convergence of the Newton-Kantorovich Method under Vertgeim Conditions: a New Improvement |
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