4Fiskom Interpolasi Tutorial

a.

n b7 1 2 16 0 2 25 1 2 54 0 2 103 1 2 212 1 2 431 0 2 860 1 2 173

cek dengan rumus10101101 173

b.

n b2 5 8 51 7 8 470 2 8 378

cek dengan rumus572 378

(10101101)2 = (...)10

an bn

(572)8=(….)10

an bn

Rumus :bn=anbn−1=an−1+βbnbn−2=an−2+βbn−1..b0=a0+βb1

Rumus :bn=anbn−1=an−1+βbnbn−2=an−2+βbn−1..b0=a0+βb1

POLINOM INTERPOLASI BEDA-TERBAGI NEWTON

Interpolasi Linear Persamaani0 1 01 3 1.09861228867

x Ralat (%)2 0.54930614433 0.69314718 20.8

Interpolasi Kuadrati ln(x) b0 4678 1.5069 1.50691 5016 1.50151 -1.5947E-052 5086 1.5005 3.721E-09

x ln(x) numerik ln(x) eksak Ralat (%)5000 1.50174597726 8.51719319 82.37

Interpolasi Kuadrati ln(x) b0 4678 1.5069 1.50691 5016 1.50151 -1.5947E-052 5086 1.5005 3.721E-09

x ln(x) numerik ln(x) eksak Ralat (%)6000 1.49065887733 8.69951475 82.87

xi ln(xi)

ln(x) numerik ln(x) eksak

xi

xi

Grafik

General Form of Newton’s Interpolating Polynomials

The first finite divided difference

The second finite divided difference

The nth finite divided difference

Graphical depiction of the recursive nature of finite divided differences

i xi f(xi) First Second Third0 1 0 0.46209812 -0.05187311 0.0078655291 4 1.3862944 0.20273255 -0.0204112 6 1.7917595 0.182321563 5 1.6094379

2 0.6931472 eksak0.6287686 numerik error= 9.29%

The first finite divided difference

The second finite divided difference

The nth finite divided difference

LAGRANGE INTERPOLATING POLYNOMIALS

i xi f(xi)0 1 01 4 1.386294361122 6 1.79175946923

x n fn(x)2 1 0.46209812037

2 0.5658443469

x f(x)=ln(x)2 0.69314718056