A stabilized gradient iteration for Ax=b adds a γAᵀA term to remove step-size tuning, but the convergence guarantee is overstated because the contraction factor still depends on α and γ.
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Stabilization of the Gradient Method for Solving Linear Algebraic Systems -- A Method Related to the Normal Equation
A stabilized gradient iteration for Ax=b adds a γAᵀA term to remove step-size tuning, but the convergence guarantee is overstated because the contraction factor still depends on α and γ.