Advertisements
Advertisements
Question
Solve using Gauss Jacobi Iteration method
2๐ + 12y + z – 4w = 13
13๐ + 5y - 3z + w = 18
2๐ + y – 3z + 9w = 31
3๐ - 4y + 10z + w = 29
Sum
Solution
`x=(18-5y+3z-w)`
`y=(13-2x-z+4w)`
`z=(29-3x+4y-w)`
`w=(31-2x-y+3z)/9`
| Iteration | x | y | z | w |
| 1 | 1.3846 | 1.0833 | 2.9 | 3.4444 |
| 2 | 1.3722 | 1.7590 | 2.5735 | 3.9831 |
| 3 | 0.9956 | 1.9679 | 2.7936 | 3.8019 |
| 4 | 0.9800 | 1.9519 | 3.0083 | 3.9357 |
| 5 | 1.0254 | 1.9812 | 2.9932 | 4.0126 |
| 6 | 1.0047 | 2.0005 | 2.9836 | 3.9942 |
| 7 | 0.9965 | 1.9987 | 2.9994 | |
| 8 | 1.0009 | 1.9984 | 3.0012 | |
| 9 | 1.0008 | 2.0000 | 2.9990 | |
| 10 | 0.9997 | 2.0001 | 2.9997 | |
| 11 | 0.9999 | 1.9999 | 3.0002 | |
| 12 | 1.0001 | 2 | 3 | |
| 13 | 1 | 2 | 3 |
∴ x = 1, y = 2, z = 3, w = 4.
shaalaa.com
Gauss Jacobi Iteration Method
Is there an error in this question or solution?
