Gauss-Seidel Fortran 90/95

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In summary, the conversation is about programming simultaneous linear equations using Fortran 90/95 and the possibility of using the Gauss Seidel iteration method. The individual is asking for clarification on how to set up a tolerance for the program and an explanation of the most common stopping criteria for the method.
  • #1
Luke1986
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Hi, I have to program using Fortran 90/95 simultaneous linear equations. My question is, is it possible to program this? First I did the inverse matrix to find the values of the solution of a 4X4 and 3X3 matrix. I set up [A][X] = [X]' and did the inverse matrix to find the values for [X]. So I got the solutions for x1 x2 x3 x4, ( numbers are subscripts ).

Now that I know that solutions exist, can I program this with the Gauss Seidel iteration method using F 90/95? May you please explain how to set up a tolerance (say 0.000001) between two iterations because I don't understand how to since I have so many variables, or what I'm looking for? I am not asking for the specific code, just a few words to clear up how to approach this program. Thanks for your help.
 
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  • #2
About the code, sure you can.
About the tolerance, the most common stopping criteria is |rk|/|r0|≤ε where ε is the desired precision of the approximation and |rk|,|r0| the norms of the residual r=b-Ax on each iteration.
 

1. What is Gauss-Seidel Fortran 90/95?

Gauss-Seidel Fortran 90/95 is a method used for solving linear systems of equations in numerical analysis. It is an iterative method that uses an initial guess to gradually improve the solution until it reaches a desired level of accuracy.

2. How does Gauss-Seidel Fortran 90/95 differ from other methods?

Gauss-Seidel Fortran 90/95 differs from other methods in that it updates the solution one variable at a time, rather than all variables at once. This makes it more efficient for large systems of equations.

3. What are the advantages of using Gauss-Seidel Fortran 90/95?

One advantage of using Gauss-Seidel Fortran 90/95 is its ability to handle large systems of equations. It also converges faster for diagonally dominant systems, and can be easily implemented in parallel computing.

4. What are the limitations of Gauss-Seidel Fortran 90/95?

Gauss-Seidel Fortran 90/95 may not converge if the system of equations is not diagonally dominant. It also requires a good initial guess to achieve accurate results, and may not converge for certain types of non-linear systems.

5. What are some real-world applications of Gauss-Seidel Fortran 90/95?

Gauss-Seidel Fortran 90/95 is commonly used in scientific and engineering fields for solving complex systems of equations. It has applications in fluid dynamics, heat transfer, and electrical circuits, among others.

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