For the purpose of this section (1.11), however, we are interested in fitting a polynomial of degree \(n − 1\) exactly through \(n\) points, and we are going to show how to do this by means of Lagrang...For the purpose of this section (1.11), however, we are interested in fitting a polynomial of degree \(n − 1\) exactly through \(n\) points, and we are going to show how to do this by means of Lagrange polynomials as an alternative to the method described above. However, in general one would expect the polynomial to be of degree \(n − 1\), and, if this is not the case, all that will happen is that we shall find that the coefficients of the highest powers of \(x\) are zero.
