On the convergence radius of the modified Newton method for multiple roots under the center–Hölder condition
Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuo...
Ausführliche Beschreibung
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| Autor*in: |
Zhou, Xiaojian [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Numerical algorithms - Springer US, 1991, 65(2013), 2 vom: 08. März, Seite 221-232 |
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| Übergeordnetes Werk: |
volume:65 ; year:2013 ; number:2 ; day:08 ; month:03 ; pages:221-232 |
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| DOI / URN: |
10.1007/s11075-013-9702-2 |
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| 520 | |a Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center–Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem. | ||
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| 650 | 4 | |a Convergence radius | |
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| 700 | 1 | |a Song, Yongzhong |4 aut | |
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10.1007/s11075-013-9702-2 doi (DE-627)OLC2051162638 (DE-He213)s11075-013-9702-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Zhou, Xiaojian verfasserin aut On the convergence radius of the modified Newton method for multiple roots under the center–Hölder condition 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2013 Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center–Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem. Nonlinear equations Multiple roots Convergence radius The modified Newton method Center–Hölder condition Chen, Xin aut Song, Yongzhong aut Enthalten in Numerical algorithms Springer US, 1991 65(2013), 2 vom: 08. März, Seite 221-232 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:65 year:2013 number:2 day:08 month:03 pages:221-232 https://doi.org/10.1007/s11075-013-9702-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2088 AR 65 2013 2 08 03 221-232 |
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Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center–Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem. © Springer Science+Business Media New York 2013 |
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Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center–Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem. © Springer Science+Business Media New York 2013 |
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Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center–Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem. © Springer Science+Business Media New York 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2051162638</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503232940.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11075-013-9702-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2051162638</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11075-013-9702-2-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Zhou, Xiaojian</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On the convergence radius of the modified Newton method for multiple roots under the center–Hölder condition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media New York 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract It is very important to enlarge the convergence ball of an iterative method. Recently, the convergence radius of the modified Newton method for finding multiple roots of nonlinear equations has been presented by Ren and Argyros when the involved function is Hölder and center–Hölder continuous. Different from the technique and the hypothesis used by them, in this paper, we also investigate the convergence radius of the modified Newton method under the condition that the derivative $f^{(m)}$ of function f satisfies the center–Hölder continuous condition. The radius given here is larger than that given by Ren and Argyros. The uniqueness ball of solution is also discussed. Some examples are given to show applications of our theorem.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multiple roots</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convergence radius</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">The modified Newton method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Center–Hölder condition</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Chen, Xin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Song, Yongzhong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Numerical algorithms</subfield><subfield code="d">Springer US, 1991</subfield><subfield code="g">65(2013), 2 vom: 08. März, Seite 221-232</subfield><subfield code="w">(DE-627)130981753</subfield><subfield code="w">(DE-600)1075844-6</subfield><subfield code="w">(DE-576)029154111</subfield><subfield code="x">1017-1398</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:65</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:2</subfield><subfield code="g">day:08</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:221-232</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11075-013-9702-2</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">65</subfield><subfield code="j">2013</subfield><subfield code="e">2</subfield><subfield code="b">08</subfield><subfield code="c">03</subfield><subfield code="h">221-232</subfield></datafield></record></collection>
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