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

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posted on 2019-08-05, 15:31 authored by Alberto Paganini, Kevin Sturm
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.

History

Citation

SIAM Journal on Numerical Analysis, 2019, 57(1), 1–26. (26 pages)

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

SIAM Journal on Numerical Analysis

Publisher

Society for Industrial and Applied Mathematics

eissn

1095-7170

Acceptance date

2018-09-27

Copyright date

2019

Available date

2019-08-05

Publisher version

https://epubs.siam.org/doi/10.1137/17M1131623

Language

en

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