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

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SUMMARY

The discussion focuses on implementing the Gauss-Seidel iteration method for solving simultaneous linear equations using Fortran 90/95. The user successfully computed solutions for 3x3 and 4x4 matrices using inverse matrices but seeks guidance on applying the Gauss-Seidel method. A key point raised is the establishment of a tolerance level, specifically 0.000001, for determining convergence, with the stopping criterion defined as |rk|/|r0|≤ε, where ε represents the desired precision.

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  • Understanding of Fortran 90/95 programming language
  • Familiarity with linear algebra concepts, particularly simultaneous linear equations
  • Knowledge of matrix operations, including inverse matrices
  • Concept of numerical methods and convergence criteria
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  • Research the implementation of the Gauss-Seidel iteration method in Fortran 90/95
  • Study numerical methods for solving linear equations, focusing on convergence criteria
  • Learn about matrix norms and their application in determining stopping conditions
  • Explore error analysis in numerical methods to understand tolerance settings
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Mathematicians, numerical analysts, and software developers working with Fortran 90/95 who are interested in solving linear equations using iterative methods.

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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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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