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

Thomas Hangelbroek (), Francis J. Narcowich (), Christian Rieger () and Joseph D. Ward ()
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Thomas Hangelbroek: University of Hawaii – Manoa, Department of Mathematics
Francis J. Narcowich: Texas A&M University, Department of Mathematics
Christian Rieger: Universität Bonn, Institut für Numerische Simulation
Joseph D. Ward: Texas A&M University, Department of Mathematics

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 517-543 from Springer

Abstract: Abstract 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 ℝ d $${\mathbb {R}}^d$$ . The kernels for which the theory applies includes the Sobolev-Matérn kernels for closed, compact, connected, C ∞ Riemannian manifolds.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_24

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DOI: 10.1007/978-3-319-72456-0_24

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