ne Lagrange quadratic interpolating polynomial through the three points(=o, go) (1, 91), and (r2, y2)is -0)(x- C-T)(- P2 (x-x1)(x-x2)( =90 +9 +y2 T0-1(0-2 1-0)(x1-2 T2-0)(2-T1 1.3 The Lagrange cubic interpolating polynomial through the four points(zo, 3o), (21, 31), I 2, 32), and(=3, 33)is P3(x)=90 r-1)x-x2)(x-03)+yy(-r0/(x1-2)(21-T3) x-T0)(-T2)(-T3 (x0-x1)(x0-x2)(x0-3) x-x0)(x-x1)(x-x3) x-r0)(x-1)(-2 +y2 (x2-x0)(x2-x1)x2-x3) t 93 (x3-x0)(x3-x1)(x3-2 132)
Example 1.7. Consider y=f(a)=cos(r)over[0.0, 1.2 (a)Use the three nodes T0=0.0, 1=0.6, and r2=1. 2 to construct a quadratic interpolation polynomial P2(a) (b)Use the four nodes 0=0.0, 1=0.4, 2=0.8, and r=1. 2 to construct a cubic interpolation polynomial P3(a)