... extreme right. For example, with N =4,x1: y1=P1P 12 x 2 : y 2 = P 2 P 123 P 23 P 123 4x3: y3= P3P 23 4P34x4: y4= P4(3.1 .2) Neville’s algorithm is a recursive way of filling in ... xN)(x 2 − x1)(x 2 − x3) (x 2 − xN)y 2 + ···+(x−x1)(x − x 2 ) (x − xN−1)(xN− x1)(xN− x 2 ) (xN− xN−1)yN(3.1.1)There are N terms, each a polynomial of degree N − 1 and ... (x1,y1);soP1=y1. Likewise defineP 2 ,P3, ,PN. Now let P 12 be the value at x of the unique polynomial ofdegree one passing through both (x1,y1) and (x 2 ,y 2 ). Likewise P 23 ,P34, ,P(N−1)N....