Abstract
Recently a new class of customized radial basis functions (RBFs) was introduced. We revisit this class of RBFs and derive a density result guaranteeing that any sufficiently smooth divergence-free function can be approximated arbitrarily closely by a linear combination of members of this class. This result has potential applications to numerically solving differential equations, such as fluid flows, whose solution is divergence free.
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References
S. Agmon, Elliptic Boundary Value Problems (Van Nostrand, New York, 1965) pp. 11–14.
S. Lowitzsch, Error estimates for matrix-valued radial basis function interpolation, J. Approx. Theory (2002) submitted.
M.J.D. Powell, The theory of radial basis approximation in 1990, in: Advances in Numerical Analysis II: Wavelets, Subdivision and Radial Basis Functions, ed. W.A. Light (Clarendon Press, Oxford, 1992) pp. 105–210.
H. Wendland, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Adv. Comput. Math. 4 (1995) 389–396.
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41Axx, 41A30, 41A35, 41A60
Svenja Lowitzsch: The results are part of the authors’s dissertation written at Texas A&M University, College Station, TX 77843, USA.
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Lowitzsch, S. A density theorem for matrix-valued radial basis functions. Numer Algor 39, 253–256 (2005). https://doi.org/10.1007/s11075-004-3641-x
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DOI: https://doi.org/10.1007/s11075-004-3641-x