= Coefficient forms from three polynomial evaluations
{title2=$a=p(0),\quad b=[p(1)-p(-1)]/2,\quad c=[p(1)+p(-1)]/2-p(0)$}
For $p(X)=a+bX+cX^2$, the three <point evaluation functionals> at $0,1,-1$ form a <basis> of the <dual space> of real <polynomials> of degree at most two. The displayed recovery formulas express the coordinate functionals, hence the <dual basis> to $1,X,X^2$, as <linear combinations> of these evaluations. More generally distinct-node <polynomial interpolation> identifies values with <coefficient> data through an invertible <Vandermonde matrix>.
Back to article page
