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Weakly-normal basis vector fields in RKHS with an application to shape Newton methods

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1137/17M1131623

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0003-3309-7657
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Journal on Numerical Analysis Journal website
Volume:
57
Issue:
1
Pages:
1–26
Publication date:
2019-01-03
Acceptance date:
2018-09-27
DOI:
EISSN:
1095-7170
ISSN:
0036-1429
Pubs id:
pubs:697726
URN:
uri:82efee79-6e70-454f-b510-f33e3ee4ea41
UUID:
uuid:82efee79-6e70-454f-b510-f33e3ee4ea41
Local pid:
pubs:697726

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