Abstract
This contribution extends earlier work [16] on interpolation/approximation by positive definite basis functions in several aspects. First, it works out the relations between various types of kernels in more detail and more generality. Second, it uses the new generality to exhibit the first example of a discontinuous positive definite function. Third, it establishes the first link from (radial) basis function theory to n-widths, and finally it uses this link to prove quasi–optimality results for approximation rates of interpolation processes and decay rates for eigenvalues of integral operators having smooth kernels.
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© 2002 Birkhäuser Verlag Basel
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Schaback, R., Wendland, H. (2002). Approximation by Positive Definite Kernels. In: Buhmann, M.D., Mache, D.H. (eds) Advanced Problems in Constructive Approximation. ISNM International Series of Numerical Mathematics, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7600-1_15
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DOI: https://doi.org/10.1007/978-3-0348-7600-1_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7602-5
Online ISBN: 978-3-0348-7600-1
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