Draft of August 17, 2001 Optimal Stability Results for Interpolation by Kernel Functions

نویسندگان

  • F. J. Narcowich
  • R. Schaback
  • J. D. Ward
چکیده

This paper proves lower bounds for the eigenvalues of positive definite matrices arising from interpolation of scattered data by positive definite kernels. By comparison with upper bounds for the interpolation error, it turns out that both bounds are asymptotically optimal for sufficiently dense data sets. Applications include interpolation on the sphere, the torus, and general Riemannian manifolds.

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تاریخ انتشار 2009