Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems

By C. Paige, Michael A. Saunders. 1982

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Citations in the corpus

Simultaneous 1D inversion of loop loop electromagnetic data for magnetic susceptibility and electrical conductivity (2003, methodology): “which we solve using the LSQR routine of Paige and Saunders (1982). This is slightly more efficient than solving equation (12) directly.”
Spectral regression: a unified subspace learning framework for content-based image retrieval (2007, background): “The remaining work load of LSQR in each iteration is 3m+5n flam [17].”
SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis (2008, background): “The remaining work load of LSQR in each iteration is 3m + 5n flam [18].”
An overview of full-waveform inversion in exploration geophysics (2009, methodology): “The linear system relating the model perturbation to the data perturbation is formed and solved with a conjugate-gradient algorithm such as LSQR (cid:1) Paige and Saunders, 1982a (cid:2) .”
Tikhonov Regularization of Large Linear Problems (2003, methodology): “This can be done in only O(� ) arithmetic floating point operations by using Givens rotations; see Eld´ en [10] and Paige and Saunders [ 20 ] for descriptions of such solution methods.”
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems (2010, methodology): “(cid:107) (cid:107) (cid:107) (cid:107) The expositions [1, 26] show that these estimates are cheaply computable in CGLS and LSQR [40, 41].”
A simple method for determining the spatial resolution of a general inverse problem (2012, methodology): “For example, for a very large and sparse linear/linearized equation, a solution may be obtained quickly by least square QR-factorization (LSQR) (Paige & Saunders 1982a,b), which has become a standard algorithm C© 2012 The Author 849 Geophysical Journal International C© 2012 RAS D ow nloaded from…”
Spectral Regression for Efficient Regularized Subspace Learning (2007, background): “The remaining work load of LSQR in each iteration is 3m + 5n flam [16].”
LSMR: An Iterative Algorithm for Sparse Least-Squares Problems (2010, unknown): “LSQR is equivalent to the conjugate-gradient (CG) method applied to the normal equation ( A T A + λ 2 I ) x = A T b .”