he Lagrange quadratic interpolating polynomial through the three points(=o, yo) C1, 91), and(2, 92)IS -31(x I --c P2(x)=0 ),(x-0(x-r1) +y1 +y2 0-了1)(0 1-3 2-0)(2-1 131) he Lagrange cubic interpolating polynomial through the four points(ro, yo), (a1,g1) 2, 12), and(=3, 33)is (x-21x-2)(x-x3)(x-20(x-2)(x-x3) 3()=90 (x0-2x1)(0-22)x0-x23) +y1 (1-x0)(x1-2)(x1-23) +y2 (x-20)(x-2x1)(x-x3) +8x-2-(132) (x2-0)(x2-1)2-x3)"°(3-0(x3-1)(x3-
Example 1.7. Consider g=f(r)=cos(a)over(0.0, 1. 2) (a) Use the three nodes 00 =0.0, 1=0.6, and 2=1.2 to construct a quadratic interpolation polynomial P2(a) (b)Use the four nodes 20=0.0, 01=0.4, 22=0.8, and r=1. 2 to construct a cubic interpolation polynomial P3(a)