@techreport{gom-sto-01-emap-tr,
  author = {Anamaria Gomide and Jorge Stolfi},
  title = {Approximation Error Maps},
  institution = {Institute of Computing, Univ. of Campinas},
  number = {IC-01-01},
  pages = {23},
  year = 2001,
  month = feb,
  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.}
}