数値解析 ヤコビ法・ガウス-ザイデル法実行例


連立一次方程式   A x = b  の反復解法

  収束しない例

A :
   1.0000000   3.0000000
   3.0000000  -2.0000000

b :
   4.0000000
   1.0000000

----- Jacobi 法 -----

0-th step :

   0.0000000
   0.0000000

1-th step :

   4.0000000
  -0.5000000

2-th step :

   5.5000000
   5.5000000

3-th step :

 -12.5000000
   7.7500000

4-th step :

 -19.2500000
 -19.2500000

5-th step :

  61.7500000
 -29.3750000

6-th step :

  92.1250000
  92.1250000

7-th step :

-272.3750000
 137.6875000

8-th step :

-409.0625000
-409.0625000

9-th step :

1231.1875000
-614.0937500

10-th step :

1846.2812500
1846.2812500

11-th step :

-5534.8437500
2768.9218750

12-th step :

-8302.7656250
-8302.7656250

13-th step :

24912.2968750
-12454.6484375

14-th step :

37367.9453125
37367.9453125

15-th step :

-112099.8359375
56051.4179688

16-th step :

-168150.2539062
-168150.2539062

17-th step :

504454.7617188
-252225.8808594

18-th step :

756681.6425781
756681.6425781

19-th step :

-2270040.9277344
1135021.9638672

20-th step :

-3405061.8916016
-3405061.8916016

(以下省略)



----- Gauss-Seidel 法 -----

0-th step :

   0.0000000
   0.0000000

1-th step :

   4.0000000
   5.5000000

2-th step :

 -12.5000000
 -19.2500000

3-th step :

  61.7500000
  92.1250000

4-th step :

-272.3750000
-409.0625000

5-th step :

1231.1875000
1846.2812500

6-th step :

-5534.8437500
-8302.7656250

7-th step :

24912.2968750
37367.9453125

8-th step :

-112099.8359375
-168150.2539062

9-th step :

504454.7617188
756681.6425781

10-th step :

-2270040.9277344
-3405061.8916016

11-th step :

10215189.6748047
15322784.0122070

12-th step :

-45968348.0366211
-68952522.5549316

13-th step :

206857571.6647949
310286356.9971924

14-th step :

-930859066.9915771
-1396288600.9873657

15-th step :

4188865806.9620972
6283298709.9431458

16-th step :

-18849896125.8294373
-28274844189.2441559

17-th step :

84824532571.7324677
127236798857.0986938

18-th step :

-381710396567.2960815
-572565594851.4440918

19-th step :

1717696784558.3322754
2576545176836.9985352

20-th step :

-7729635530506.9960938
-11594453295760.9941406

(以下省略)

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