4Fiskom Interpolasi Tutorial
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Transcript of 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