Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods
We present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133–148, 2016] by proving a general asymptotic result for orbits of an operator acting on a reflexive Banach space. This result is obtained under a condition i...
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| Format: | Journal article |
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Yokohama Publishers
2017
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| _version_ | 1826278723731587072 |
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| author | Badea, C Seifert, D |
| author_facet | Badea, C Seifert, D |
| author_sort | Badea, C |
| collection | OXFORD |
| description | We present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133–148, 2016] by proving a general asymptotic result for orbits of an operator acting on a reflexive Banach space. This result is obtained under a condition involving the growth of the resolvent, and we also discuss conditions involving the location and the geometry of the numerical range of the operator. We then apply the general results to some classes of iterative projection methods in approximation theory, such as the Douglas-Rachford splitting method and, under suitable geometric conditions either on the ambient Banach space or on the projection operators, the method of alternating projections. |
| first_indexed | 2024-03-06T23:48:13Z |
| format | Journal article |
| id | oxford-uuid:71adc81f-345e-493b-9a69-66ca3bc36cb7 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:48:13Z |
| publishDate | 2017 |
| publisher | Yokohama Publishers |
| record_format | dspace |
| spelling | oxford-uuid:71adc81f-345e-493b-9a69-66ca3bc36cb72022-03-26T19:45:16ZQuantified asymptotic behaviour of Banach space operators and applications to iterative projection methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:71adc81f-345e-493b-9a69-66ca3bc36cb7Symplectic Elements at OxfordYokohama Publishers2017Badea, CSeifert, DWe present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133–148, 2016] by proving a general asymptotic result for orbits of an operator acting on a reflexive Banach space. This result is obtained under a condition involving the growth of the resolvent, and we also discuss conditions involving the location and the geometry of the numerical range of the operator. We then apply the general results to some classes of iterative projection methods in approximation theory, such as the Douglas-Rachford splitting method and, under suitable geometric conditions either on the ambient Banach space or on the projection operators, the method of alternating projections. |
| spellingShingle | Badea, C Seifert, D Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods |
| title | Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods |
| title_full | Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods |
| title_fullStr | Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods |
| title_full_unstemmed | Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods |
| title_short | Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods |
| title_sort | quantified asymptotic behaviour of banach space operators and applications to iterative projection methods |
| work_keys_str_mv | AT badeac quantifiedasymptoticbehaviourofbanachspaceoperatorsandapplicationstoiterativeprojectionmethods AT seifertd quantifiedasymptoticbehaviourofbanachspaceoperatorsandapplicationstoiterativeprojectionmethods |