On convergence of regularized modified Newton's method for nonlinear ill-posed problems
In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the...
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| Autor*in: |
George, Santhosh [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Walter de Gruyter GmbH & Co. KG ; 2010 |
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| Schlagwörter: |
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| Anmerkung: |
© de Gruyter 2010 |
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| Umfang: |
14 |
| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Journal of inverse and ill-posed problems - Berlin : de Gruyter, 1993, 18(2010), 2 vom: 31. Mai, Seite 133-146 |
| Übergeordnetes Werk: |
volume:18 ; year:2010 ; number:2 ; day:31 ; month:05 ; pages:133-146 ; extent:14 |
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| DOI / URN: |
10.1515/jiip.2010.004 |
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NLEJ247090522 |
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| 245 | 1 | 0 | |a On convergence of regularized modified Newton's method for nonlinear ill-posed problems |
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| 520 | |a In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. | ||
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10.1515/jiip.2010.004 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090522 DE-627 ger DE-627 rakwb George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems Walter de Gruyter GmbH & Co. KG 2010 14 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2010 In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. Walter de Gruyter Online Zeitschriften Tihkonov regularization regularized Newton's method balancing principle Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 18(2010), 2 vom: 31. Mai, Seite 133-146 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:18 year:2010 number:2 day:31 month:05 pages:133-146 extent:14 https://doi.org/10.1515/jiip.2010.004 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 18 2010 2 31 05 133-146 14 |
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10.1515/jiip.2010.004 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090522 DE-627 ger DE-627 rakwb George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems Walter de Gruyter GmbH & Co. KG 2010 14 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2010 In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. Walter de Gruyter Online Zeitschriften Tihkonov regularization regularized Newton's method balancing principle Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 18(2010), 2 vom: 31. Mai, Seite 133-146 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:18 year:2010 number:2 day:31 month:05 pages:133-146 extent:14 https://doi.org/10.1515/jiip.2010.004 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 18 2010 2 31 05 133-146 14 |
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10.1515/jiip.2010.004 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090522 DE-627 ger DE-627 rakwb George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems Walter de Gruyter GmbH & Co. KG 2010 14 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2010 In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. Walter de Gruyter Online Zeitschriften Tihkonov regularization regularized Newton's method balancing principle Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 18(2010), 2 vom: 31. Mai, Seite 133-146 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:18 year:2010 number:2 day:31 month:05 pages:133-146 extent:14 https://doi.org/10.1515/jiip.2010.004 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 18 2010 2 31 05 133-146 14 |
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10.1515/jiip.2010.004 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090522 DE-627 ger DE-627 rakwb George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems Walter de Gruyter GmbH & Co. KG 2010 14 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2010 In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. Walter de Gruyter Online Zeitschriften Tihkonov regularization regularized Newton's method balancing principle Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 18(2010), 2 vom: 31. Mai, Seite 133-146 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:18 year:2010 number:2 day:31 month:05 pages:133-146 extent:14 https://doi.org/10.1515/jiip.2010.004 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 18 2010 2 31 05 133-146 14 |
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10.1515/jiip.2010.004 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090522 DE-627 ger DE-627 rakwb George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems Walter de Gruyter GmbH & Co. KG 2010 14 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2010 In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. Walter de Gruyter Online Zeitschriften Tihkonov regularization regularized Newton's method balancing principle Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 18(2010), 2 vom: 31. Mai, Seite 133-146 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:18 year:2010 number:2 day:31 month:05 pages:133-146 extent:14 https://doi.org/10.1515/jiip.2010.004 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 18 2010 2 31 05 133-146 14 |
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On convergence of regularized modified Newton's method for nonlinear ill-posed problems |
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In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. © de Gruyter 2010 |
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In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. © de Gruyter 2010 |
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In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order. © de Gruyter 2010 |
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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">NLEJ247090522</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820030141.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2010 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/jiip.2010.004</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">artikel_Grundlieferung.pp</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ247090522</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="100" ind1="1" ind2=" "><subfield code="a">George, Santhosh</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On convergence of regularized modified Newton's method for nonlinear ill-posed problems</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">14</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">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© de Gruyter 2010</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδ ∈ Y with ‖y – yδ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Walter de Gruyter Online Zeitschriften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tihkonov regularization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">regularized Newton's method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">balancing principle</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of inverse and ill-posed problems</subfield><subfield code="d">Berlin : de Gruyter, 1993</subfield><subfield code="g">18(2010), 2 vom: 31. Mai, Seite 133-146</subfield><subfield code="w">(DE-627)NLEJ248236091</subfield><subfield code="w">(DE-600)2041913-2</subfield><subfield code="x">1569-3945</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:18</subfield><subfield code="g">year:2010</subfield><subfield code="g">number:2</subfield><subfield code="g">day:31</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:133-146</subfield><subfield code="g">extent:14</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/jiip.2010.004</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DGR</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">18</subfield><subfield code="j">2010</subfield><subfield code="e">2</subfield><subfield code="b">31</subfield><subfield code="c">05</subfield><subfield code="h">133-146</subfield><subfield code="g">14</subfield></datafield></record></collection>
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