Simple intuitive/graphical interpretation of the Gauss-Seidel method

In summary, The conversation is about the application of Gauss Seidel iterative method for solving systems of linear equations and the request for a graphical or intuitive interpretation. The person asking the question also wonders about the methodology and why nobody is replying to their question.
  • #1
O.J.
199
0
Hi,
I am currently studying the application of Gauss Seidel iterative method for solving systems of linear equations and am having trouble understanding the principle behind it. Can some1 provide any graphical or intuitive interpretation??
thank you
 
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  • #2
anyone?
 
  • #3
In other words, in the same way you can illustrates Newton's method of using the first order linearization of a function at a point to draw a tangent that intersects the x-axis at a point close to the solution (and you can get infinitely closer by infinitely doing more iterations), how can you illustrate gauss seidel method?>
 
  • #4
?/
 
  • #5
I wondered about this too for a while but didnt come up with anything and gave up.
 
  • #6
did you try asking here? i treid graphing 2 equations with 2 variables but things get messy and i can't get wats happening... i can't believe no1 here knows the catch to it... :s
 
  • #7
Someone please answer my question: could you offer an intuitive explanation for the methodology of gaus seidel iterative approach for solving systems of equations? thank u
 
  • #8
why is NO ONE replying?///
 
  • #9
O.J. said:
why is NO ONE replying?///

Probably because no one here knows the answer, or perhaps because there is no good answer. Numerical analysis is not a strongpoint of these forums, from my experience.
 

1. What is the Gauss-Seidel method?

The Gauss-Seidel method is an iterative algorithm used to solve a system of linear equations. It is an improvement on the Gauss-Jordan method, as it converges faster and is better suited for systems with a large number of equations.

2. How does the Gauss-Seidel method work?

The Gauss-Seidel method works by repeatedly updating the values of the variables in a system of equations, using the values from the previous iteration. It starts with an initial guess for the variables and then uses the updated values to calculate new values until the desired level of accuracy is achieved.

3. What is the difference between the Gauss-Seidel method and the Jacobi method?

The main difference between the Gauss-Seidel method and the Jacobi method is that the Gauss-Seidel method uses the updated values from the previous iteration, while the Jacobi method uses the original values from the previous iteration. This makes the Gauss-Seidel method converge faster, but it also requires more memory and is more prone to errors.

4. How do I interpret the results of the Gauss-Seidel method?

The results of the Gauss-Seidel method are the values of the variables in the system of equations, which should satisfy all of the equations in the system. If the method converges, the values should be close to the exact solution. However, it is important to check for convergence and accuracy, as the method may not always give the exact solution.

5. Can the Gauss-Seidel method be used for non-linear systems?

No, the Gauss-Seidel method is only applicable to linear systems. For non-linear systems, other methods such as Newton's method or the fixed-point iteration method should be used.

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