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Método de Jacobi Final

The document contains a matrix and then data showing the convergence of a function over iterations. The matrix and data are for modeling some unknown process as it approaches a steady state over time.

Uploaded by

Gilbert Peña Timoteo
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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40 views11 pages

Método de Jacobi Final

The document contains a matrix and then data showing the convergence of a function over iterations. The matrix and data are for modeling some unknown process as it approaches a steady state over time.

Uploaded by

Gilbert Peña Timoteo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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X1 X2 X3 X4 X5

4 -1 0 -1 0
-1 4 -1 0 -1
0 -1 4 0 0
-1 0 0 4 -1
0 -1 0 -1 4
0 0 -1 0 -1

K X1 X2 X3 X4 X5
0 0 0 0 0 0
1 0 1.25 0 1.5 -0.5
2 0.6875 1.125 0.6875 1.375 0.5625
3 0.625 1.734375 0.625 1.8125 0.46875
4 0.88671875 1.6796875 0.88671875 1.7734375 0.83984375
5 0.86328125 1.903320313 0.86328125 1.931640625 0.806640625
6 0.958740234 1.883300781 0.958740234 1.917480469 0.941650391
7 0.950195313 1.964782715 0.950195313 1.975097656 0.92956543
8 0.984970093 1.957489014 0.984970093 1.969940186 0.978744507
9 0.9818573 1.987171173 0.9818573 1.99092865 0.974342346
10 0.994524956 1.984514236 0.994524956 1.989049911 0.992257118
11 0.993391037 1.995326757 0.993391037 1.996695518 0.990653515
12 0.998005569 1.994358897 0.998005569 1.996011138 0.997179449
13 0.997592509 1.998297647 0.997592509 1.998796254 0.996595293
14 0.999273475 1.997945078 0.999273475 1.998546951 0.998972539
15 0.999123007 1.999379872 0.999123007 1.999561504 0.998759745
16 0.999735344 1.99925144 0.999735344 1.999470688 0.99962572
17 0.999680532 1.999774102 0.999680532 1.999840266 0.999548204
18 0.999903592 1.999727317 0.999903592 1.999807184 0.999863658
19 0.999883625 1.999917711 0.999883625 1.999941813 0.999835421
20 0.999964881 1.999900668 0.999964881 1.999929762 0.999950334
21 0.999957607 1.999970024 0.999957607 1.999978804 0.999940048
22 0.999987207 1.999963816 0.999987207 1.999974414 0.999981908
23 0.999984557 1.99998908 0.999984557 1.999992279 0.999978161
24 0.99999534 1.999986819 0.99999534 1.99999068 0.999993409
25 0.999994375 1.999996022 0.999994375 1.999997187 0.999992044
26 0.999998302 1.999995198 0.999998302 1.999996605 0.999997599
27 0.999997951 1.999998551 0.999997951 1.999998975 0.999997102
28 0.999999382 1.999998251 0.999999382 1.999998763 0.999999125
29 0.999999254 1.999999472 0.999999254 1.999999627 0.999998944
30 0.999999775 1.999999363 0.999999775 1.999999549 0.999999681
31 0.999999728 1.999999808 0.999999728 1.999999864 0.999999615
32 0.999999918 1.999999768 0.999999918 1.999999836 0.999999884
33 0.999999901 1.99999993 0.999999901 1.99999995 0.99999986
34 0.99999997 1.999999915 0.99999997 1.99999994 0.999999958
35 0.999999964 1.999999974 0.999999964 1.999999982 0.999999949
36 0.999999989 1.999999969 0.999999989 1.999999978 0.999999985
37 0.999999987 1.999999991 0.999999987 1.999999993 0.999999981
38 0.999999996 1.999999989 0.999999996 1.999999992 0.999999994
39 0.999999995 1.999999997 0.999999995 1.999999998 0.999999993
40 0.999999999 1.999999996 0.999999999 1.999999997 0.999999998
41 0.999999998 1.999999999 0.999999998 1.999999999 0.999999998
42 0.999999999 1.999999999 0.999999999 1.999999999 0.999999999
43 0.999999999 2 0.999999999 2 0.999999999
44 1 1.999999999 1 2 1
45 1 2 1 2 1
46 1 2 1 2 1
47 1 2 1 2 1
48 1 2 1 2 1
49 1 2 1 2 1
50 1 2 1 2 1
51 1 2 1 2 1
52 1 2 1 2 1
X6 = B 𝑋^((𝐾+1))=𝑇 〖 (𝑋) 〗 ^𝐾+𝐶
0 0 SÍ
0 5 SÍ
-1 0 SÍ
0 6 SÍ
-1 -2 SÍ
4 6 SÍ

X1 X2 X3
X6 0 0.6875 0.625
0 1.25 1.125 1.734375
1.5 0 0.6875 0.625
1.375 1.5 1.375 1.8125
1.8125 -0.5 0.5625 0.46875
1.7734375 1.5 1.375 1.8125
1.931640625
1.917480469
1.975097656
1.969940186
1.99092865
1.989049911
1.996695518
1.996011138
1.998796254
1.998546951
1.999561504
1.999470688
1.999840266
1.999807184
1.999941813
1.999929762
1.999978804
1.999974414
1.999992279
1.99999068
1.999997187
1.999996605
1.999998975
1.999998763
1.999999627
1.999999549
1.999999864
1.999999836
1.99999995
1.99999994
1.999999982
1.999999978
1.999999993
1.999999992
1.999999998
1.999999997
1.999999999
1.999999999
2
2
2
2
2
2
2
2
2
2
)=𝑇 〖 (𝑋) 〗 ^𝐾+𝐶
0
1.25
C 0
1.5
-0.5
1.5

X4 X5 X6 X7 X8
0.88671875 0.86328125 0.958740234
1.6796875 1.903320313 1.883300781
0.88671875 0.86328125 0.958740234
1.7734375 1.931640625 1.917480469
0.83984375 0.806640625 0.941650391
1.7734375 1.931640625 1.917480469
X1 X2 X3 X4 X5
10 -1 2 0 0
-1 11 -1 3 0
2 -1 10 -1 0
0 3 -1 8 0
0 0 0 0 0
0 0 0 0 0

K X1 X2 X3 X4 X5
0 0 0 0 0 0
1 0.6 2.272727273 -1.1 1.875 0
2 1.047272727 1.715909091 -0.80522727 0.885227273 0
3 0.932636364 2.053305785 -1.04934091 1.130880682 0
4 1.01519876 1.953695764 -0.96810863 0.973842717 0
5 0.988991302 2.011414726 -1.0102859 1.02135051 0
6 1.003198653 1.992241261 -0.99452174 0.99443374 0
7 0.998128473 2.002306882 -1.00197223 1.00359431 0
8 1.000625134 1.998670301 -0.99903558 0.998888391 0
9 0.999674145 2.000447672 -1.00036916 1.00061919 0
10 1.000118599 1.999767947 -0.99982814 0.999785978 0
11 0.999942423 2.000084775 -1.00006833 1.000108502 0
12 1.000022143 1.999958963 -0.99996916 0.999959669 0
13 0.999989728 2.000015816 -1.00001257 1.000019244 0
14 1.000004095 1.999992675 -0.99999444 0.999992498 0
15 0.999998155 2.000002924 -1.0000023 1.000003442 0
16 1.000000753 1.999998684 -0.99999899 0.999998616 0
17 0.999999667 2.000000537 -1.00000042 1.000000619 0
18 1.000000138 1.999999763 -0.99999982 0.999999746 0
19 0.99999994 2.000000098 -1.00000008 1.000000112 0
20 1.000000025 1.999999957 -0.99999997 0.999999954 0
21 0.999999989 2.000000018 -1.00000001 1.00000002 0
22 1 1.999999992 -0.99999999 0.999999992 0
23 1 2 -1 1 0
24 1 2 -1 1 0
25 1 2 -1 1 0
26 1 2 -1 1 0
27 1 2 -1 1 0
28 1 2 -1 1 0
29 1 2 -1 1 0
X6 = C
0 6 SÍ
0 25 SÍ
0 -11 SÍ
0 15 SÍ
0 0 SÍ
0 0 SÍ

X1 X2 X3
X6 0.6 1.047272727 0.932636364
0 2.272727273 1.715909091 2.053305785
0 -1.1 -0.80522727 -1.04934091
0 1.875 0.885227273 1.130880682
0 0 0 0
0 0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.6
2.272727273
C -1.1
1.875
0
0

X4 X5 X6 X7 X8 X9 X10
1.01519876 0.988991302 1.003198653 0.9981284734 1.0006251343 0.9996741452 1.0001185987
1.953695764 2.011414726 1.992241261 2.0023068816 1.9986703011 2.0004476715 1.999767947
-0.96810863 -1.0102859 -0.99452174 -1.001972231 -0.999035576 -1.000369158 -0.999828143
0.973842717 1.02135051 0.99443374 1.0035943102 0.9988883906 1.0006191901 0.9997859785
0 0 0 0 0 0 0
0 0 0 0 0 0 0
X1 X2 X3 X4 X5 X6
3 -0.1 -0.2 0 0 0
0.1 7 -0.3 0 0 0
0.3 -0.2 10 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0

K X1 X2 X3 X4 X5 X6
0 0 0 0 0 0 0
1 2.616666667 -2.75714286 7.14 0 0 0
2 3.000761905 -2.48852381 7.006357143 0 0 0
3 3.000806349 -2.49973844 7.000206667 0 0 0
4 3.000022497 -2.50000266 6.999981041 0 0 0
5 2.999998647 -2.50000113 6.999999272 0 0 0
6 2.999999914 -2.50000001 7.000000018 0 0 0
7 3 -2.5 7 0 0 0
8 3 -2.5 7 0 0 0
9 3 -2.5 7 0 0 0
10 3 -2.5 7 0 0 0
11 3 -2.5 7 0 0 0
12 3 -2.5 7 0 0 0
13 3 -2.5 7 0 0 0
14 3 -2.5 7 0 0 0
15 3 -2.5 7 0 0 0
16 3 -2.5 7 0 0 0
17 3 -2.5 7 0 0 0
18 3 -2.5 7 0 0 0
19 3 -2.5 7 0 0 0
20 3 -2.5 7 0 0 0
21 3 -2.5 7 0 0 0
22 3 -2.5 7 0 0 0
23 3 -2.5 7 0 0 0
24 3 -2.5 7 0 0 0
25 3 -2.5 7 0 0 0
26 3 -2.5 7 0 0 0
27 3 -2.5 7 0 0 0
28 3 -2.5 7 0 0 0
29 3 -2.5 7 0 0 0
= B
7.85 SÍ
-19.3 SÍ
71.4 SÍ C
0 SÍ
0 SÍ
0 SÍ

X1 X2 X3 X4 X5
2.616666667 3.000761905 3.000806349 3.000022497 2.999998647
-2.75714286 -2.48852381 -2.49973844 -2.50000266 -2.50000113
7.14 7.006357143 7.000206667 6.999981041 6.999999272
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
2.616666667
-2.75714286
7.14
0
0
0

X6 X7 X8 X9 X10
2.999999914 3 3 3 3
-2.50000001 -2.5 -2.5 -2.5 -2.5
7.000000018 7 7 7 7
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0

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