Estimates for Local Approximations of Functions on Differential Manifold

We obtain an estimate for the convergence rate of approximation of functions on a differentiable manifold We consider two approaches to approximation of such functions. The first is based on approximate relations for the manifold and is independent of a given set of plane approximations. The second...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2021-09, Vol.257 (5), p.624-651
Main Author: Dem’yanovich, Yu. K.
Format: Article
Language:English
Subjects:
Approximation
Interpolation
Mathematical analysis
Mathematics
Mathematics and Statistics
Spline functions
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Summary:We obtain an estimate for the convergence rate of approximation of functions on a differentiable manifold We consider two approaches to approximation of such functions. The first is based on approximate relations for the manifold and is independent of a given set of plane approximations. The second is based on approximations of functions in the plane. We consider the approximation of Courant type on the n-dimensional sphere, in the projective space, and also for the Zlamal approximation and interpolation splines.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05514-z