# A Stabilized GMRES Method for Solving Underdetermined Least Squares Problems

@article{Liao2020ASG, title={A Stabilized GMRES Method for Solving Underdetermined Least Squares Problems}, author={Ze-Yu Liao and K. Hayami and K. Morikuni and Jun-Feng Yin}, journal={ArXiv}, year={2020}, volume={abs/2007.10853} }

Consider using the right-preconditioned generalized minimal residual (AB-GMRES) method, which is an efficient method for solving underdetermined least squares problems. Morikuni (Ph.D. thesis, 2013) showed that for some inconsistent and ill-conditioned problems, the iterates of the AB-GMRES method may diverge. This is mainly because the Hessenberg matrix in the GMRES method becomes very ill-conditioned so that the backward substitution of the resulting triangular system becomes numerically… Expand

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