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
Hence, indeed, by minimizing the approximation error over the training set of operator evaluations, the interpolation error
is also kept small.
1 and provides the interpolation error
estimate from Lemma 2.
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.