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We analyze the convergence of the Conjugate Gradient (CG) method in exactarithmetic, when the coefficient matrix $A$ is symmetric positive semidefiniteand the system is consistent. To do so, we diagonalize $A$ and decompose thealgorithm into the range and the null space components of $A$. Further, weapply the analysis to the CGLS and CGNE (CG Normal Error) methods forrank-deficient least squares problems.

Convergence of the Conjugate Gradient Method on Singular Systems