ABSTRACT
The matrix B is non-singular if and only if the set of points {x\,... , %drn} is a
drn (A nf){x) = ^ 2 vibi(x), where B\ = f . (3.3)
The norm of the interpolation operator is then
||A«II = max ||B_ 1b(a;)||i. (3.4)
This follows because, as is easily seen, the ‘fundamental Lagrange polynomial’
associated with the point xj is (B~1b)j. The value of ||An| depends on the fundamental system {^i, ... , xj^ }• The
norm ||An| can be made arbitrarily large if the fundamental system is badly
chosen. The interesting question is how small ||An| can be made by a good choice of fundamental system, especially for r = 3.
