= Fekete interpolation sites for a continuous function space
{c}
{title2=$\max_{x_1,\ldots,x_n}|\det(\phi_j(x_i))|$}
For a real $n$-dimensional <vector space> of <continuous functions> on a <compact> <interval>, choose sites maximizing the absolute evaluation <determinant> in any <basis>. <Linear independence> ensures some nonzero evaluation <determinant>, so a maximizer exists and has distinct sites. Replacing row $i$ by evaluation at $t$ multiplies the <determinant> by the cardinal function $\ell_i(t)$. Maximality implies $|\ell_i(t)|\le1$, hence the <Lebesgue constant of interpolation> is at most $n$. This gives a useful interpolation set without asserting that determinant maximization minimizes the <Lebesgue constant of interpolation>.
Back to article page
