Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 33, Issue 3, Pages 849-874Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drs026
Keywords
Quasiinterpolation; Riemannian Data; Geodesic Finite Elements; Approximation Order; Riemannian Center of Mass
Categories
Funding
- European Research Council [ERC AdG 247277]
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We consider quasi-interpolation operators for functions assuming their values in a Riemannian manifold. We construct such operators from corresponding linear quasi-interpolation operators by replacing affine averages with the Riemannian centre of mass. As a main result, we show that the approximation rate of such a nonlinear operator is the same as for the linear operator it has been derived from. In order to formulate this result in an intrinsic way, we use the Sasaki metric to compare the derivatives of the function to be approximated with the derivatives of the nonlinear approximant. Numerical experiments confirm our theoretical findings.
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