On convergence of regularized modified Newton's method for nonlinear ill-posed problems
Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ δ and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert sp...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
George, Santhosh [verfasserIn] |
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| Format: |
Artikel |
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| Erschienen: |
2010 |
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| Anmerkung: |
© de Gruyter 2010 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of inverse and ill-posed problems - Walter de Gruyter GmbH & Co. KG, 1993, 18(2010), 2 vom: Mai, Seite 133-146 |
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| Übergeordnetes Werk: |
volume:18 ; year:2010 ; number:2 ; month:05 ; pages:133-146 |
| Links: |
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| DOI / URN: |
10.1515/jiip.2010.004 |
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OLC2140619471 |
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| 520 | |a Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ 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 (DE-627)OLC2140619471 (DE-B1597)jiip.2010.004-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © de Gruyter 2010 Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ 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. Enthalten in Journal of inverse and ill-posed problems Walter de Gruyter GmbH & Co. KG, 1993 18(2010), 2 vom: Mai, Seite 133-146 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:18 year:2010 number:2 month:05 pages:133-146 https://doi.org/10.1515/jiip.2010.004 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_60 GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_2020 GBV_ILN_4277 AR 18 2010 2 05 133-146 |
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10.1515/jiip.2010.004 doi (DE-627)OLC2140619471 (DE-B1597)jiip.2010.004-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn George, Santhosh verfasserin aut On convergence of regularized modified Newton's method for nonlinear ill-posed problems 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © de Gruyter 2010 Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ 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. Enthalten in Journal of inverse and ill-posed problems Walter de Gruyter GmbH & Co. KG, 1993 18(2010), 2 vom: Mai, Seite 133-146 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:18 year:2010 number:2 month:05 pages:133-146 https://doi.org/10.1515/jiip.2010.004 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_60 GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_2020 GBV_ILN_4277 AR 18 2010 2 05 133-146 |
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Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ 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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Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ 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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Abstract 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 $ y^{δ} $ ∈ Y with ‖y – $ y^{δ} $ ‖ ≤ 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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