I have coded up a toy implementation of Conjugate Residual and have been testing it.  Both wikipedia and the Saad claim that Conjugate Residual and Conjugate Gradient have similar convergence behavior.  For some examples I have been doing I haven't found this to be true.  For a $128 \times 128$ symmetric indefinite matrix, I don't get (machine) convergence at 400 iterations.  This is at odds with my understanding of Conjugate residual being a Krylov space method that should converge in at most 128 iterations.  (The condition number of this matrix is about 120 and every singular value  is repeated since the eigenvalues come in positive and negative pairs.)I am guessing the statement about similar convergence properties refers to the performance on symmetric positive definite matrices, and numerical experiments are consistent with this.So my question is, what determines the convergence rate of conjugate residual for a symmetric but indefinite matrix?  Also, is the conjugate residual method supposed to converge in at most $n$ iterations, where $n$ is the size of the system?
Does Conjugate Residual really have convergence properties similar to that of Conjugate Gradient?
linear algebra;linear solver;iterative method;krylov method