Abstract
AbstractIn [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449–469], the authors analyzed the convergence behavior of the generalized minimal residual (GMRES) method for the least squares problem , where A ∈ Rn × n may be singular and , by decomposing the algorithm into the range and its orthogonal complement components. However, we found that the proof of the fact that GMRES gives a least squares solution if was not complete. In this article, we will give a complete proof.
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