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Metnum (interpolasi)
1.
INTERPOLASI (METODE NUMERIK) Erik
Pebrinasyah Ali Martun Pulungan Nyella Kenanga Andini Dwi Yulia Ningsih Ario Amanda
2.
Tentukakanan lah 5
titik Interpolasi (sebarang titik) dari data berikut dengan mengugunakan 4 metode yaitu 1. Interpolasi Liner x y 2. Interpolasi kuadrat 15 14944 20 19867 3. Interpolasi Newton 25 24740 4. Interpolasi Lagrange 30 29552 35 34290 40 38945 45 43497 50 47943 55 52269 60 56464 (Sumber: Nasution;54)
3.
Penyelesaian : Misalkan diambil
sembarang lima titik interpolasi yaitu 18, 23,33,43, dan 53. 1. Interpolasi Linier Untuk x = 18 X0 = 15 → f(x0) = 14944 X1 = 20 → f(x1) = 19867
4.
Untuk x
= 23 X0 = 20 → f(x0) = 19867 X1 = 25 → f(x1) = 24740 Untuk x = 33 X0 = 30 → f(x0) = 29552 X1 = 35 → f(x1) = 34290
5.
Untuk x
= 43 X0 = 40 → f(x0) = 38945 X1 = 45 → f(x1) = 43497 Untuk x = 53 X0 = 50→ f(x0) = 47934 X1 = 55 → f(x1) = 52269
6.
Tabel Interpolasi linier
7.
2. Interpolasi Kuadrat
Untuk x = 18 X0 = 15 → f(x0) = 14944 X1 = 20 → f(x1) = 19867 X2 = 25 → f(x2) = 24740 b0 = f(x0) = 14944 b1 = = 984,6 b2 = = =-1
8.
F (x)
= b0 + b1 ( x – x0) + b2 (x-x0)(x-x1) = 14944 + 984,6(18-15) + (-1)(18-15)(18-20) = 14944 + 984,6 (3) + (-1)(3)(-2) = 14944 + 2953,8 + 6 = 17903,8 Untuk x = 23 X0 = 20 ,f(x0 ) =19867 X1 = 25 ,f(x1 ) =24740 X2 = 30 ,f(x2 ) =29552 b0 = f(x0 ) = 19867
9.
b1 = = = 974,6 b2 = = = = -1,22 F (x) = b0 + b1(x- x0) + b2(x- x0) (x- x1) = 19867 + 974.6 (23-20) + (-1.22)(23-20)(23-25) = 19867 + 2923.8 + 7.32 = 22798.12 Untuk x = 33 X0 = 30 , f(x0 ) =29552 X1 = 35 ,f(x1 ) =34290 X2 = 40 ,f(x2 ) =38945 b0 = f(x0 ) = 29552
10.
b1 =
= 947,6 b2 = = = -1,66 F (x) = b0 + b1(x- x0) + b2(x- x0) (x- x1) = 29552 + 947.6 (33-30) + (-1.66)(33-30)(33-35) = 29552 + 2842.8 + 9.96 = 32404.76 untuk x = 43 X0 = 40 → f(x0) = 38945 X1 = 45 → f(x1) = 43497 X2 = 50 → f(x2) = 47943 b0 = f(x0) = 38945
11.
b1 =
= = 910,4 b2 = = = -2,12 F (x) = b0 + b1 ( x – x0) + b2 (x-x0)(x-x1) = 38945 + 910,4(43-40) + (-2,12)(43-40)(43-45) = 38945 + 910,4 (3) + (-2,12)(3)(-2) = 38945 + 2731,2 + 12,72 = 41688,92 Untuk x =53 X0 = 50 → f(x0) = 47943 X1 = 55 → f(x1) = 52269 X2 = 60 → f(x2) = 56464
12.
b0 =
f(x0) = 47943 b1 = = 865,2 b2 = = -13,1 F (x) = b0 + b1 ( x – x0) + b2 (x-x0)(x-x1) = 47943 + 865,2(53-50) + (-13,1)(53-50)(53-55) = 47943 + 2595,6 + 78,6 = 50617,2
13.
Tabel Interpolasi Kuadrat
14.
3. Interpolasi newton.
15.
16.
17.
18.
19.
Tabel Hasil Interpolasi
Newton
20.
4. Interpolasi
Lagrange
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Tabel Hasil Interpolasi Lagrange
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