Solve Equations 2x+5y=16,3x+y=11 using Gauss Seidel method
Solution:
Total Equations are `2`
`2x+5y=16`
`3x+y=11`
The coefficient matrix of the given system is not diagonally dominant.
Hence, we re-arrange the equations as follows, such that the elements in the coefficient matrix are diagonally dominant.
`3x+y=11`
`2x+5y=16`
From the above equations
`x_(k+1)=1/3(11-y_(k))`
`y_(k+1)=1/5(16-2x_(k+1))`
Initial gauss `(x,y) = (0,0)`
Solution steps are
`1^(st)` Approximation
`x_1=1/3[11-(0)]=1/3[11]=3.6667`
`y_1=1/5[16-2(3.6667)]=1/5[8.6667]=1.7333`
`2^(nd)` Approximation
`x_2=1/3[11-(1.7333)]=1/3[9.2667]=3.0889`
`y_2=1/5[16-2(3.0889)]=1/5[9.8222]=1.9644`
`3^(rd)` Approximation
`x_3=1/3[11-(1.9644)]=1/3[9.0356]=3.0119`
`y_3=1/5[16-2(3.0119)]=1/5[9.9763]=1.9953`
`4^(th)` Approximation
`x_4=1/3[11-(1.9953)]=1/3[9.0047]=3.0016`
`y_4=1/5[16-2(3.0016)]=1/5[9.9968]=1.9994`
`5^(th)` Approximation
`x_5=1/3[11-(1.9994)]=1/3[9.0006]=3.0002`
`y_5=1/5[16-2(3.0002)]=1/5[9.9996]=1.9999`
`6^(th)` Approximation
`x_6=1/3[11-(1.9999)]=1/3[9.0001]=3`
`y_6=1/5[16-2(3)]=1/5[9.9999]=2`
Solution By Gauss Seidel Method.
`x=3~=3`
`y=2~=2`
Iterations are tabulated as below
| Iteration | x | y |
| 1 | 3.6667 | 1.7333 |
| 2 | 3.0889 | 1.9644 |
| 3 | 3.0119 | 1.9953 |
| 4 | 3.0016 | 1.9994 |
| 5 | 3.0002 | 1.9999 |
| 6 | 3 | 2 |
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
