Extensions of The Method
Like other iterative methods, GMRES is usually combined with a preconditioning method in order to speed up convergence.
The cost of the iterations grow as O(n2), where n is the iteration number. Therefore, the method is sometimes restarted after a number, say k, of iterations, with xk as initial guess. The resulting method is called GMRES(k) or Restarted GMRES.
Read more about this topic: Generalized Minimal Residual Method
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