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 225 articles , 1 standard article )

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  1. Adcock, Ben; Platte, Rodrigo B.: A mapped polynomial method for high-accuracy approximations on arbitrary grids (2016)
  2. Andreev, Roman: Wavelet-in-time multigrid-in-space preconditioning of parabolic evolution equations (2016)
  3. 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)
  4. Bello Cruz, J.Y.; Ferreira, O.P.; Prudente, L.F.: On the global convergence of the inexact semi-smooth Newton method for absolute value equation (2016)
  5. Greif, C.; Paige, C.C.; Titley-Peloquin, D.; Varah, J.M.: Numerical equivalences among Krylov subspace algorithms for skew-symmetric matrices (2016)
  6. Hajarian, Masoud: Least squares solution of the linear operator equation (2016)
  7. Hannukainen, A.; Harhanen, L.; Hyvönen, N.; Majander, H.: Edge-promoting reconstruction of absorption and diffusivity in optical tomography (2016)
  8. Huang, Guangxin; Reichel, Lothar; Yin, Feng: On the choice of solution subspace for nonstationary iterated Tikhonov regularization (2016)
  9. Li, Jiao-fen; Li, Wen; Huang, Ru: An efficient method for solving a matrix least squares problem over a matrix inequality constraint (2016)
  10. Mittal, A.; Chen, X.; Tong, A.H.; Iaccarino, G.: A flexible uncertainty propagation framework for general multiphysics systems (2016)
  11. van Leeuwen, T.; Herrmann, F.J.: A penalty method for PDE-constrained optimization in inverse problems (2016)
  12. Xie, Pengpeng; Wei, Yimin: The stability of formulae of the Gohberg-Semencul-Trench type for Moore-Penrose and group inverses of Toeplitz matrices (2016)
  13. Yang, Hu; Wang, Shaoxin: A flexible condition number for weighted linear least squares problem and its statistical estimation (2016)
  14. 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)
  15. Baboulin, M.; Dongarra, J.; Lacroix, R.: Computing least squares condition numbers on hybrid multicore/GPU systems (2015)
  16. Borges, Leonardo S.; Viloche Bazán, Fermín S.; Cunha, Maria C.C.: Automatic stopping rule for iterative methods in discrete ill-posed problems (2015)
  17. Calvetti, Daniela; Somersalo, Erkki: Statistical methods in imaging (2015)
  18. Chung, Julianne; Knepper, Sarah; Nagy, James G.: Large-scale inverse problems in imaging (2015)
  19. Chung, Julianne M.; Kilmer, Misha E.; O’Leary, Dianne P.: A framework for regularization via operator approximation (2015)
  20. Conder, James A.: Fitting multiple Bell curves stably and accurately to a time series as applied to Hubbert cycles or other phenomena (2015)

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