After how many iterations does the gs algorithm within the while loop come to an end?

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It is impossible to determine how many iterations the Gauss-Seidel algorithm within the while loop will take to come to an end without knowing the specific problem and parameters being solved. The convergence of the algorithm depends on the initial guess, the matrix being solved, and other factors. It is also possible that the algorithm may not converge at all for certain matrices or initial guesses.