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- W1983886273 abstract "An iterative method LSMR is presented for solving linear systems $Ax=b$ and least-squares 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 $A^T! Ax = A^T! b$, so that the quantities $|A^T! r_k|$ are monotonically decreasing (where $r_k = b - Ax_k$ is the residual for the current iterate $x_k$). We observe in practice that $|r_k|$ also decreases monotonically, so that compared to LSQR (for which only $|r_k|$ is monotonic) it is safer to terminate LSMR early. We also report some experiments with reorthogonalization." @default.
- W1983886273 created "2016-06-24" @default.
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- W1983886273 date "2011-01-01" @default.
- W1983886273 modified "2023-10-14" @default.
- W1983886273 title "LSMR: An Iterative Algorithm for Sparse Least-Squares Problems" @default.
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- W1983886273 doi "https://doi.org/10.1137/10079687x" @default.
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