@techreport{TR-IC-01-01,
  number = {IC-01-01},
  author = {Anamaria Gomide and Jorge Stolfi},
  title = {Approximation Error Maps},
  month = {February},
  year = {2001}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 23 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      Let $F$ and $A$ be two linear function spaces defined on some
      domain $\Omega$. Let $\left\|\cdot\right\|$ be a vector
      semi-norm for the space $A+F$. We consider here the question of
      how well $A$ approximates $F$ in the sense of the metric
      $\left\|\cdot\right\|$. Global error measures are insufficiently
      informative when the space $A$ is not spatially homogeneous. We
      introduce here the concept of {\em approximation error map}, a
      mathematical description of how the approximation errors are
      distributed over the domain --- not for a single function $f\in
      F$, but for all such functions at once. We illustrate this
      concept by computing the error maps of several harmonic spline
      spaces on the circle and on the sphere.
  }
}