Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds

abstract

• Springer International Publishing AG, part of Springer Nature 2018. All rights reserved. This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approximation spaces spanned by local Lagrange functions which are spatially highly localized. The construction of such functions is computationally efficient and generalizes the construction given in Hangelbroek et al. (Math Comput, 2017, in press) for restricted surface splines on d. The kernels for which the theory applies includes the Sobolev-Matrn kernels for closed, compact, connected, C Riemannian manifolds.

authors

• Narcowich, Francis

author list (cited authors)

• Hangelbroek, T., Narcowich, F. J., Rieger, C., & Ward, J. D.

citation count

• 1

complete list of authors

• Hangelbroek, Thomas||Narcowich, Francis J||Rieger, Christian||Ward, Joseph D

publication date

• January 2018

publisher

• Springer Nature  Publisher

keywords

• 41a17, 41a27, 41a63
• Math.ca
• Math.na

Digital Object Identifier (DOI)

• 10.1007/978-3-319-72456-0_24

start page

• 517

end page

• 543

URL

• http://dx.doi.org/10.1007/978-3-319-72456-0_24