Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems. An iterative method is given for solving Ax = b and min|| Ax - b||2 , where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing LSQR with several other conjugate-gradient algorithms, indicating that LSQR is the most reliable algorithm when A is ill-conditioned.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 231 articles , 1 standard article )

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  3. Adcock, Ben; Platte, Rodrigo B.: A mapped polynomial method for high-accuracy approximations on arbitrary grids (2016)
  4. Andreev, Roman: Wavelet-in-time multigrid-in-space preconditioning of parabolic evolution equations (2016)
  5. Bazán, Fermín S.V.; Kleefeld, Andreas; Leem, Koung Hee; Pelekanos, George: Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers (2016)
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  12. Hannukainen, A.; Hyvönen, N.; Majander, H.; Tarvainen, T.: Efficient inclusion of total variation type priors in quantitative photoacoustic tomography (2016)
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  14. Li, Jiao-fen; Li, Wen; Huang, Ru: An efficient method for solving a matrix least squares problem over a matrix inequality constraint (2016)
  15. Mittal, A.; Chen, X.; Tong, A.H.; Iaccarino, G.: A flexible uncertainty propagation framework for general multiphysics systems (2016)
  16. van Leeuwen, T.; Herrmann, F.J.: A penalty method for PDE-constrained optimization in inverse problems (2016)
  17. Xie, Pengpeng; Wei, Yimin: The stability of formulae of the Gohberg-Semencul-Trench type for Moore-Penrose and group inverses of Toeplitz matrices (2016)
  18. Yang, Hu; Wang, Shaoxin: A flexible condition number for weighted linear least squares problem and its statistical estimation (2016)
  19. Zhang, Xiaowei; Cheng, Li; Chu, Delin; Liao, Li-Zhi; Ng, Michael K.; Tan, Roger C.E.: Incremental regularized least squares for dimensionality reduction of large-scale data (2016)
  20. Baboulin, M.; Dongarra, J.; Lacroix, R.: Computing least squares condition numbers on hybrid multicore/GPU systems (2015)

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