What if Jacobi Method's condition did not met?

[abrowaqas]

what if Jacobi Method's condition did not meet?

Homework Statement

solve by Jacobi Method upto four decimal places

8x+y-z= 8
2x+y+9z= 12
x-8y+12z = 35

Homework Equations

The Attempt at a Solution

since the condition of convergence of jacobi method is

|A1| > |B1|+|C1|
|B2|> |A2|+|C2|
|C3|> |A3|+|B3|

since this condition doesn't satisfy in the above question ; hence when i started iterations the values vary in every iteration...

what i do to this question to make it possible to use jacobi method here in this question?

 

[mighty2000]

Hello,

Thank you for posting your question on the forum. I would like to address your concern about the Jacobi Method. First, let me clarify that the Jacobi Method is an iterative numerical method used to solve a system of linear equations. It is known to converge under certain conditions, as you have mentioned in your post. However, there are cases where the condition is not met, and the method may not converge to a solution.

In your given system of equations, the condition is not met, and as a result, the method may not converge. This could be due to various reasons, such as the coefficients of the equations being too large or small, or the equations being ill-conditioned. In such cases, it is not possible to use the Jacobi Method to solve the system of equations.

To make it possible to use the Jacobi Method in this question, you could try scaling the equations to bring the coefficients to a more suitable range. This can be done by dividing each equation by the largest coefficient in that equation. However, this may not always guarantee convergence, and it is best to try other methods of solving the system of equations, such as Gauss-Seidel or Gauss-Jordan elimination.

In conclusion, as a scientist, it is important to be aware of the limitations and conditions of different methods and to choose the most appropriate method for a given problem. I hope this helps in solving your question. If you have any further queries, please feel free to ask.