# LSMR: An iterative algorithm for sparse least-squares problems

@article{Fong2010LSMRAI, title={LSMR: An iterative algorithm for sparse least-squares problems}, author={D. C. Fong and M. Saunders}, journal={ArXiv}, year={2010}, volume={abs/1006.0758} }

An iterative method LSMR is presented for solving linear systems Ax = b and leastsquares problems min ‖Ax−b‖2, with A being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is analytically equivalent to the MINRES method applied to the normal equation ATAx = ATb, so that the quantities ‖Ark‖ are monotonically decreasing (where rk = b−Axk is the residual for the current iterate xk). We observe in practice that ‖rk‖ also decreases monotonically, so… Expand

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