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III. Lampiran GD Metode Gauss dan Gauss Jordan >> A=[1 2 1 4 2 0 4 3 4 2 2 1 -3 1 3 2] A = 1 2 1 4 2 0 4 3 4 2 2 1 -3 1 3 2 >> b=[13 28 20 6] b = 13 28
| Date post: | 17-Jan-2016 |
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III. Lampiran
GD
Metode Gauss dan Gauss Jordan
>> A=[1 2 1 4
2 0 4 3
4 2 2 1
-3 1 3 2]
A =
1 2 1 4
2 0 4 3
4 2 2 1
-3 1 3 2
>> b=[13
28
20
6]
b =
13
28
20
6
>> A=[A b]
A =
1 2 1 4 13
2 0 4 3 28
4 2 2 1 20
-3 1 3 2 6
>> A(1,:)=A(1,:)/A(1,1)
A =
1 2 1 4 13
2 0 4 3 28
4 2 2 1 20
-3 1 3 2 6
>> A(2,:)=A(2,:)-A(1,:)*2
A =
1 2 1 4 13
0 -4 2 -5 2
4 2 2 1 20
-3 1 3 2 6
>> A(3,:)=A(3,:)-A(1,:)*4
A =
1 2 1 4 13
0 -4 2 -5 2
0 -6 -2 -15 -32
-3 1 3 2 6
>> A(4,:)=A(4,:)-A(1,:)*-3
A =
1 2 1 4 13
0 -4 2 -5 2
0 -6 -2 -15 -32
0 7 6 14 45
>> A(2,:)=A(2,:)/-4
A =
1.0000 2.0000 1.0000 4.0000 13.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 -6.0000 -2.0000 -15.0000 -32.0000
0 7.0000 6.0000 14.0000 45.0000
>> A(3,:)=A(3,:)-A(2,:)*A(3,2)
A =
1.0000 2.0000 1.0000 4.0000 13.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 0 -5.0000 -7.5000 -35.0000
0 7.0000 6.0000 14.0000 45.0000
>> A(4,:)=A(4,:)-A(2,:)*A(4,2)
A =
1.0000 2.0000 1.0000 4.0000 13.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 0 -5.0000 -7.5000 -35.0000
0 0 9.5000 5.2500 48.5000
>> A(3,:)=A(3,:)/A(3,3)
A =
1.0000 2.0000 1.0000 4.0000 13.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 0 1.0000 1.5000 7.0000
0 0 9.5000 5.2500 48.5000
>> A(4,:)=A(4,:)-A(3,:)*A(4,3)
A =
1.0000 2.0000 1.0000 4.0000 13.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 0 1.0000 1.5000 7.0000
0 0 0 -9.0000 -18.0000
>> A(4,:)=A(4,:)/A(4,4)
A =
1.0000 2.0000 1.0000 4.0000 13.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 0 1.0000 1.5000 7.0000
0 0 0 1.0000 2.0000
>> A(1,:)=A(1,:)-A(2,:)*A(1,2)
A =
1.0000 0 2.0000 1.5000 14.0000
0 1.0000 -0.5000 1.2500 -0.5000
0 0 1.0000 1.5000 7.0000
0 0 0 1.0000 2.0000
>> A(1,:)=A(1,:)-A(3,:)*A(1,3)
A =
1.0000 0 0 -1.5000 0
0 1.0000 -0.5000 1.2500 -0.5000
0 0 1.0000 1.5000 7.0000
0 0 0 1.0000 2.0000
>> A(2,:)=A(2,:)-A(3,:)*A(2,3)
A =
1.0000 0 0 -1.5000 0
0 1.0000 0 2.0000 3.0000
0 0 1.0000 1.5000 7.0000
0 0 0 1.0000 2.0000
>> A(1,:)=A(1,:)-A(4,:)*A(1,4)
A =
1.0000 0 0 0 3.0000
0 1.0000 0 2.0000 3.0000
0 0 1.0000 1.5000 7.0000
0 0 0 1.0000 2.0000
>> A(2,:)=A(2,:)-A(4,:)*A(2,4)
A =
1.0000 0 0 0 3.0000
0 1.0000 0 0 -1.0000
0 0 1.0000 1.5000 7.0000
0 0 0 1.0000 2.0000
>> A(3,:)=A(3,:)-A(4,:)*A(3,4)
A =
1 0 0 0 3
0 1 0 0 -1
0 0 1 0 4
0 0 0 1 2
>> X2=A(:,5)
X2 =
3
-1
4
2
>> A=[1 2 1 4
2 0 4 3
4 2 2 1
-3 1 3 2]
A =
1 2 1 4
2 0 4 3
4 2 2 1
-3 1 3 2
>> b=[13
28
20
6]
b =
13
28
20
6
>> X=A\b
X =
3.0000
-1.0000
4.0000
2.0000
>> A=[1 2 1 4
2 0 4 3
4 2 2 1
-3 1 3 2]
A =
1 2 1 4
2 0 4 3
4 2 2 1
-3 1 3 2
>> b=[13
28
20
6]
b =
13
28
20
6
>> X=A\b
X =
3.0000
-1.0000
4.0000
2.0000
>> [Q,R]=qr(A)
Q =
-0.1826 0.6509 0.2135 0.7053
-0.3651 -0.1719 -0.8559 0.3232
-0.7303 0.3930 0.0217 -0.5583
0.5477 0.6263 -0.4705 -0.2939
R =
-5.4772 -1.2780 -1.4606 -1.4606
0 2.7142 2.6282 3.7335
0 0 -4.5781 -2.6330
0 0 0 2.6448
>> y=Q'*b
y =
-23.9172
15.2656
-23.5786
5.2895
>> X3=R\y
X3 =
3.0000
-1.0000
4.0000
2.0000
>> [L,U]=lu(A)
L =
0.2500 0.6000 -0.4583 1.0000
0.5000 -0.4000 1.0000 0
1.0000 0 0 0
-0.7500 1.0000 0 0
U =
4.0000 2.0000 2.0000 1.0000
0 2.5000 4.5000 2.7500
0 0 4.8000 3.6000
0 0 0 3.7500
>> y=L\b
y =
20.0000
21.0000
26.4000
7.5000
>> X2=U\y
X2 =
3.0000
-1.0000
4.0000
2.0000
UGD
>> A=[37 21 20 0; 15 27 11 10;17 13 18 29; 0 23 21 28]
A =
37 21 20 0
15 27 11 10
17 13 18 29
0 23 21 28
>> b=[4360
4020
4540
4780]
b =
4360
4020
4540
4780
>> X=A\b
X =
40.0000
80.0000
60.0000
60.0000
>> [Q,R]=qr(A)
Q =
-0.8527 0.2290 -0.0352 0.4683
-0.3457 -0.5517 0.6940 -0.3075
-0.3918 -0.0116 -0.5358 -0.7479
0 -0.8019 -0.4797 0.3561
R =
-43.3935 -32.3320 -27.9074 -14.8179
0 -28.6817 -18.5379 -28.3075
0 0 -12.7877 -22.0298
0 0 0 -14.7920
>> y=Q'*b
y =
1.0e+003 *
-6.8858
-5.1053
-2.0891
-0.8875
>> X2=R\y
X2 =
40.0000
80.0000
60.0000
60.0000
>> A=[37 21 20 0; 15 27 11 10;17 13 18 29; 0 23 21 28]
A =
37 21 20 0
15 27 11 10
17 13 18 29
0 23 21 28
>> b=[4360
4020
4540
4780]
b =
4360
4020
4540
4780
>> A=[A b]
A =
37 21 20 0 4360
15 27 11 10 4020
17 13 18 29 4540
0 23 21 28 4780
>> A(1,:)=A(1,:)/A(1,1)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0.0150 0.0270 0.0110 0.0100 4.0200
0.0170 0.0130 0.0180 0.0290 4.5400
0 0.0230 0.0210 0.0280 4.7800
>> A(2,:)=A(2,:)-A(1,:)*A(2,1)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0185 0.0029 0.0100 2.2524
0.0170 0.0130 0.0180 0.0290 4.5400
0 0.0230 0.0210 0.0280 4.7800
>> A(3,:)=A(3,:)-A(1,:)*A(3,1)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0185 0.0029 0.0100 2.2524
0 0.0034 0.0088 0.0290 2.5368
0 0.0230 0.0210 0.0280 4.7800
>> A(2,:)=A(2,:)/A(2,2)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0010 0.0002 0.0005 0.1218
0 0.0034 0.0088 0.0290 2.5368
0 0.0230 0.0210 0.0280 4.7800
>> A(3,:)=A(3,:)-A(2,:)*A(3,2)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0010 0.0002 0.0005 0.1218
0 0 0.0083 0.0272 2.1284
0 0.0230 0.0210 0.0280 4.7800
>> A(4,:)=A(4,:)-A(2,:)*A(4,2)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0010 0.0002 0.0005 0.1218
0 0 0.0083 0.0272 2.1284
0 0 0.0174 0.0156 1.9776
>> A(3,:)=A(3,:)/A(3,3)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0010 0.0002 0.0005 0.1218
0 0 0.0010 0.0033 0.2569
0 0 0.0174 0.0156 1.9776
>> A(4,:)=A(4,:)-A(3,:)*A(4,3)
A =
1.0e+003 *
0.0010 0.0006 0.0005 0 0.1178
0 0.0010 0.0002 0.0005 0.1218
0 0 0.0010 0.0033 0.2569
0 0 0 -0.0415 -2.4921
>> A(4,:)=A(4,:)/A(4,4)
A =
1.0000 0.5676 0.5405 0 117.8378
0 1.0000 0.1564 0.5409 121.8421
0 0 1.0000 3.2809 256.8525
0 0 0 1.0000 60.0000
>> A(1,:)=A(1,:)-A(2,:)*A(1,2)
A =
1.0000 0 0.4518 -0.3070 48.6842
0 1.0000 0.1564 0.5409 121.8421
0 0 1.0000 3.2809 256.8525
0 0 0 1.0000 60.0000
>> A(1,:)=A(1,:)-A(3,:)*A(1,3)
A =
1.0000 0 0 -1.7892 -67.3500
0 1.0000 0.1564 0.5409 121.8421
0 0 1.0000 3.2809 256.8525
0 0 0 1.0000 60.0000
>> A(2,:)=A(2,:)-A(3,:)*A(2,3)
A =
1.0000 0 0 -1.7892 -67.3500
0 1.0000 0 0.0277 81.6620
0 0 1.0000 3.2809 256.8525
0 0 0 1.0000 60.0000
>> A(1,:)=A(1,:)-A(4,:)*A(1,4)
A =
1.0000 0 0 0 40.0000
0 1.0000 0 0.0277 81.6620
0 0 1.0000 3.2809 256.8525
0 0 0 1.0000 60.0000
>> A(2,:)=A(2,:)-A(4,:)*A(2,4)
A =
1.0000 0 0 0 40.0000
0 1.0000 0 0 80.0000
0 0 1.0000 3.2809 256.8525
0 0 0 1.0000 60.0000
>> A(3,:)=A(3,:)-A(4,:)*A(3,4)
A =
1.0000 0 0 0 40.0000
0 1.0000 0 0 80.0000
0 0 1.0000 0 60.0000
0 0 0 1.0000 60.0000
>> X3=A(:,5)
X3 =
40.0000
80.0000
60.0000
60.0000
