Optimal convergence rates for Tikhonov regularization in Besov scales
In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that...
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Gespeichert in:
| Autor*in: |
Lorenz, D. A. [verfasserIn] Trede, D. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Walter de Gruyter GmbH & Co. KG ; 2009 |
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| Schlagwörter: |
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| Anmerkung: |
© de Gruyter 2009 |
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| Umfang: |
8 |
| 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, 17(2009), 1 vom: 04. Feb., Seite 69-76 |
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volume:17 ; year:2009 ; number:1 ; day:04 ; month:02 ; pages:69-76 ; extent:8 |
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10.1515/JIIP.2009.008 |
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NLEJ247090018 |
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| 520 | |a In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. | ||
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10.1515/JIIP.2009.008 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090018 DE-627 ger DE-627 rakwb Lorenz, D. A. verfasserin aut Optimal convergence rates for Tikhonov regularization in Besov scales Walter de Gruyter GmbH & Co. KG 2009 8 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2009 In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. Walter de Gruyter Online Zeitschriften Tikhonov regularization Besov space scales of Banach spaces convergence rate Trede, D. verfasserin aut Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 17(2009), 1 vom: 04. Feb., Seite 69-76 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:17 year:2009 number:1 day:04 month:02 pages:69-76 extent:8 https://doi.org/10.1515/JIIP.2009.008 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 17 2009 1 04 02 69-76 8 |
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10.1515/JIIP.2009.008 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090018 DE-627 ger DE-627 rakwb Lorenz, D. A. verfasserin aut Optimal convergence rates for Tikhonov regularization in Besov scales Walter de Gruyter GmbH & Co. KG 2009 8 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2009 In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. Walter de Gruyter Online Zeitschriften Tikhonov regularization Besov space scales of Banach spaces convergence rate Trede, D. verfasserin aut Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 17(2009), 1 vom: 04. Feb., Seite 69-76 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:17 year:2009 number:1 day:04 month:02 pages:69-76 extent:8 https://doi.org/10.1515/JIIP.2009.008 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 17 2009 1 04 02 69-76 8 |
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10.1515/JIIP.2009.008 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090018 DE-627 ger DE-627 rakwb Lorenz, D. A. verfasserin aut Optimal convergence rates for Tikhonov regularization in Besov scales Walter de Gruyter GmbH & Co. KG 2009 8 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2009 In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. Walter de Gruyter Online Zeitschriften Tikhonov regularization Besov space scales of Banach spaces convergence rate Trede, D. verfasserin aut Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 17(2009), 1 vom: 04. Feb., Seite 69-76 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:17 year:2009 number:1 day:04 month:02 pages:69-76 extent:8 https://doi.org/10.1515/JIIP.2009.008 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 17 2009 1 04 02 69-76 8 |
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10.1515/JIIP.2009.008 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090018 DE-627 ger DE-627 rakwb Lorenz, D. A. verfasserin aut Optimal convergence rates for Tikhonov regularization in Besov scales Walter de Gruyter GmbH & Co. KG 2009 8 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2009 In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. Walter de Gruyter Online Zeitschriften Tikhonov regularization Besov space scales of Banach spaces convergence rate Trede, D. verfasserin aut Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 17(2009), 1 vom: 04. Feb., Seite 69-76 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:17 year:2009 number:1 day:04 month:02 pages:69-76 extent:8 https://doi.org/10.1515/JIIP.2009.008 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 17 2009 1 04 02 69-76 8 |
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10.1515/JIIP.2009.008 doi artikel_Grundlieferung.pp (DE-627)NLEJ247090018 DE-627 ger DE-627 rakwb Lorenz, D. A. verfasserin aut Optimal convergence rates for Tikhonov regularization in Besov scales Walter de Gruyter GmbH & Co. KG 2009 8 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2009 In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. Walter de Gruyter Online Zeitschriften Tikhonov regularization Besov space scales of Banach spaces convergence rate Trede, D. verfasserin aut Enthalten in Journal of inverse and ill-posed problems Berlin : de Gruyter, 1993 17(2009), 1 vom: 04. Feb., Seite 69-76 (DE-627)NLEJ248236091 (DE-600)2041913-2 1569-3945 nnns volume:17 year:2009 number:1 day:04 month:02 pages:69-76 extent:8 https://doi.org/10.1515/JIIP.2009.008 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 17 2009 1 04 02 69-76 8 |
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Optimal convergence rates for Tikhonov regularization in Besov scales |
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In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. © de Gruyter 2009 |
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In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. © de Gruyter 2009 |
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In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales. © de Gruyter 2009 |
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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">NLEJ247090018</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820030137.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2009 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/JIIP.2009.008</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)NLEJ247090018</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">Lorenz, D. A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Optimal convergence rates for Tikhonov regularization in Besov scales</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">8</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 2009</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates and vice versa. Moreover, we present optimal source conditions for regularization in Besov scales.</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">Tikhonov regularization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Besov space</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">scales of Banach spaces</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">convergence rate</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Trede, D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</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">17(2009), 1 vom: 04. Feb., Seite 69-76</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:17</subfield><subfield code="g">year:2009</subfield><subfield code="g">number:1</subfield><subfield code="g">day:04</subfield><subfield code="g">month:02</subfield><subfield code="g">pages:69-76</subfield><subfield code="g">extent:8</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/JIIP.2009.008</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">17</subfield><subfield code="j">2009</subfield><subfield code="e">1</subfield><subfield code="b">04</subfield><subfield code="c">02</subfield><subfield code="h">69-76</subfield><subfield code="g">8</subfield></datafield></record></collection>
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