LSMR
LSMR: an iterative algorithm for sparse least-squares problems. 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.
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References in zbMATH (referenced in 35 articles , 1 standard article )
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- Chung, Julianne; Palmer, Katrina: A hybrid LSMR algorithm for large-scale Tikhonov regularization (2015)
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