Approximation in Normed Spaces
Overview
Distance
Let K be a subset of a normed space X. Then the function , d(x,K), called the
distance from {% x \in X %} to K is defined to be
{% d(x,K) := inf_{y \in K} ||x-y|| %}
Best Approximation
The best approximation of an element x by an element {% y \in K %} is an
element {% y %} such that
{% ||x-y|| = d(x,K) %}
