Matrix-valued radial basis functions: Stability estimates and applications

DOI10.1007/s10444-004-1786-8zbMath1070.65007OpenAlexW2031178557MaRDI QIDQ1776157

Svenja Lowitzsch

Publication date: 20 May 2005

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-004-1786-8

zbMATH Keywords

interpolationstabilityincompressible Navier-Stokes equationsdivergence-freematrix-valued radial basis functions

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05)

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Cites Work

• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices
• A practical guide to splines
• Error estimates for interpolation by compactly supported radial basis functions of minimal degree
• Error estimates and condition numbers for radial basis function interpolation
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Error estimates for matrix-valued radial basis function interpolation
• Norms of inverses and condition numbers for matrices associated with scattered data
• Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions