@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.
}
}