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Finally, we have investigated some PSI errors--fringe interpolation errors and bull's-eye patterns (from coherent scattering)--that have no direct analogy in the autocollimator.
Nevertheless, weighted polynomial interpolation at approximate Fekete points shows small Lebesgue constants, close to those of nonweighted polynomial interpolation (growth like O(logn)), and the best interpolation errors also for small [epsilon].
The variability in this error was about 16 percent of that for the SRTM, suggesting that interpolation error makes up only a modest component of the observed differences between SRTM and the Oakland elevations.
1), the trace theorem, and a standard interpolation error estimate that
Hence, indeed, by minimizing the approximation error over the training set of operator evaluations, the interpolation error is also kept small.
1) with both the exact finite element error and interpolation error measured in the norms inherited by the problem.
Hermite's representation of the interpolation error
For functions f (x) which are analytic in a large neighbourhood of the interval, this gives rise to an interpolation error which is very uniform on the interval, as opposed to interpolation in equidistant points, which leads to the Runge phenomenon (extreme oscillations between interpolation points).
1]y regular function on one of the domains described in the previous sections, is contained, up to the interpolation error, in its values at relatively few Xu points.
I] is the interpolation error, which we bound in [section]2.
In Section 3 we give some anisotropic interpolation error estimates for Clement type interpolation and prove the uniform discrete inf-sup condition.