Analysis of the Truncated Conjugate Gradient Method for Linear Matrix Equations

The matrix-oriented version of the conjugate gradient (CG) method can be used to approximate solution certain linear matrix equations. To limit memory consumption, low-rank reduction factored iterates is often employed, possibly leading disruption regular convergence behavior. We analyze properties in regime and identify quantities that are responsible for early termination, usually stagnation, when truncation effect. Moreover, we illustrate relations between CG a projection technique directly applied same equation.