Math 6610 • Analysis of Numerical Methods I

{The interpolant to symmetric data is symmetric} Suppose you are
given symmetric data
\[
  (x_i,y_i),\qquad i=-n,-n+1,\cdots,n-1,n,
  \tag{3}
\]
such that
\[
  x_{-i}=-x_i,\qquad \text{and}\qquad y_{-i}=y_i\qquad
  i=0,1,\cdots,n.
  \tag{4}
\]
What is the required degree of the interpolating polynomial \(p\)? Show that the
interpolating polynomial is even, i.e.,
\[
  p(x)=p(-x)
  \tag{5}
\]
for all real numbers \(x\).