Fortran Can You Implement Gauss-Seidel Iteration in Fortran 90/95?

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The discussion centers on programming simultaneous linear equations using Fortran 90/95, specifically through the Gauss-Seidel iteration method. The user has successfully solved 3x3 and 4x4 matrices using inverse matrices and is now seeking guidance on implementing the Gauss-Seidel method. They are particularly interested in establishing a tolerance level of 0.000001 for convergence between iterations. The response highlights that a common stopping criterion for this method is based on the residuals, expressed as |rk|/|r0|≤ε, where ε represents the desired precision and |rk| and |r0| are the norms of the residuals at each iteration. This approach provides a clear framework for assessing convergence in the iterative process.
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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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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.
 
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