Question

er Lagrange ,Divided difference and Hermitewatnejed, Jnp 1.5, and x2-2, andf (x)ssin(x) * Given the point sx.-1, a) Find its Lagrange interpolation P on these points b) Write its newton's divided difference P, polynomial c)Write Hermite Hs by Using part a outcomes d) Write Hermite Hi by Using part b outcomes Rules: Lagrange form of Hermite polynomial of degre at most 2n-+1 Here, L., (r) denotes the Lagrange coefficient polynomial of degree n. If ec la.bl, then the error formula is given by E.ir'(2.)!)) (x-x.)..(x-r"). for some ξ(x ) in (a,b). Lagrange polynomial r (x-x where P. (a Divided-Diference relationship Divided-Difference Form of the Hermite Polynomial: where zn®:24.-x, and/Iu ,z2ial=/txaJ for each k=0,...-"

Answer 1

SOLUTION

: 52 nang es İmlenpolalion: x 04l + Gs- (1-s-2) (2-1) (1 -1-s) Newton's Divided d erou u Disseneuis table: 0 841 0 312 0 4 88 A S 0.99 2 O9 09 0 48 = o.g41 0.3122-0.312

mite intenbolaien; o 909 -041 O 013 mu take