Weakly-normal basis vector fields in RKHS with an application to shape Newton methods
We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show how to approximate the...
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2019
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| _version_ | 1797079089663705088 |
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| author | Paganini, A Sturm, K |
| author_facet | Paganini, A Sturm, K |
| author_sort | Paganini, A |
| collection | OXFORD |
| description | We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show how to approximate them. Then, we employ this basis to discretise shape Newton methods and investigate the impact of this discretisation on convergence rates. |
| first_indexed | 2024-03-07T00:40:42Z |
| format | Journal article |
| id | oxford-uuid:82efee79-6e70-454f-b510-f33e3ee4ea41 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:40:42Z |
| publishDate | 2019 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:82efee79-6e70-454f-b510-f33e3ee4ea412022-03-26T21:40:56ZWeakly-normal basis vector fields in RKHS with an application to shape Newton methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:82efee79-6e70-454f-b510-f33e3ee4ea41Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2019Paganini, ASturm, KWe construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show how to approximate them. Then, we employ this basis to discretise shape Newton methods and investigate the impact of this discretisation on convergence rates. |
| spellingShingle | Paganini, A Sturm, K Weakly-normal basis vector fields in RKHS with an application to shape Newton methods |
| title | Weakly-normal basis vector fields in RKHS with an application to shape Newton methods |
| title_full | Weakly-normal basis vector fields in RKHS with an application to shape Newton methods |
| title_fullStr | Weakly-normal basis vector fields in RKHS with an application to shape Newton methods |
| title_full_unstemmed | Weakly-normal basis vector fields in RKHS with an application to shape Newton methods |
| title_short | Weakly-normal basis vector fields in RKHS with an application to shape Newton methods |
| title_sort | weakly normal basis vector fields in rkhs with an application to shape newton methods |
| work_keys_str_mv | AT paganinia weaklynormalbasisvectorfieldsinrkhswithanapplicationtoshapenewtonmethods AT sturmk weaklynormalbasisvectorfieldsinrkhswithanapplicationtoshapenewtonmethods |