Barycentric interpolation is a method of interpolation that evaluates a Lagrange interpolating
polynomial using precomputed weights. For distinct
nodes 
, ..., 
and values 
,
..., 
, its second barycentric form is
 |
for 
, where 
and 
. The expression evaluates the unique polynomial
of polynomial degree at most 
that interpolates the data (Berrut and Trefethen 2004).
The weights depend only on the nodes, so they can be reused for different data values on the same nodes. Once the weights
have been computed, each evaluation takes 
arithmetic operations. Multiplying all weights
by the same nonzero factor leaves the result unchanged. This formulation avoids repeatedly
forming products for each evaluation, but it does not remove the sensitivity associated
with an unfavorable choice of nodes (Berrut and Trefethen 2004).
