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Projection-based Quasiinterpolation in Manifolds

by P. Grohs and M. Sprecher

(Report number 2013-23)

Abstract
We consider the problem of approximating manifold-valued functions with approximation spaces spanned by linear combinations of cardinal B-splines with control points constrained to lie on the manifold, followed by a closest-point projection onto the manifold. Under certain conditions we can prove that these spaces realize the optimal approximation rate. Applications for denoising of manifold-valued data and the computation of geometric variational problems are discussed.

Keywords: Riemannian data, manifold-valued function, approximation, quasiinterpolation, B-spline, variational problems

@Techreport{GS13_520,
  author = {P. Grohs and M. Sprecher},
  title = {Projection-based Quasiinterpolation in Manifolds},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2013-23},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2013/2013-23.pdf },
  year = {2013}
}

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