LSMR: An Iterative Algorithm for Sparse Least-Squares Problems

By David Chin-Lung Fong, Michael A. Saunders. SIAM Journal on Scientific Computing, 2010

488 citations recorded by the source corpus.

Abstract A new two-step discrete method is proposed in this paper for reconstruction of three-dimensional temperature distribution in an absorbing, emitting and isotropically scattering medium. With this new method, the temperature of the wall is also considered. The local radiative source term is reconstructed in the first step through the discrete transfer method from the directional, exit radiation intensities measured by CCD cameras. Then, the temperature of each discrete element is calculated in the second step by subtracting the scattering contribution from the retrieved radiative source term through the discrete ordinate method. The least squares minimum residual algorithm is employed to solve the ill-posed reconstruction equations and the calculation is improved to reduce the computational cost. The performance of the proposed method is examined by numerical test problems with unimodal and bimodal temperature distributions. The ill-conditioning of the reconstruction problem is checked by the Picard condition. The effects of the measurement noise and the radiative properties on the reconstruction accuracy are discussed. The results show that the method proposed in this paper is capable of reconstructing the temperature distribution accurately in large, confined, participating media, even with noisy input data. The computation time reduction of this new method is significant when compared with other methods.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/38fb6b42f4c1cd1aa9ba2c54821c3fd42e6235f7

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Citations in the corpus

Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, methodology): “Thus, appropriate numerical methods for minimum-length linear least squares problems are iterative solvers such as LSQR [99] and LSMR [49], which produce sequences of residual error vectors.”
Structural damage detection by a new iterative regularization method and an improved sensitivity function (2017, methodology): “The LSMR method in fact attempts to obtain ak in the k iteration as an approximate solution of the damage equation through the l2-minimization of Sek [37].”
EKTELO: A Framework for Defining Differentially-Private Computations (2018, methodology): “nd MT v until convergence. The time complexity of these methods isO(kn2)for dense matrix representations where k is the number of iterations. In experiments we use a well-known iterative method, LSMR [16]. Empirically, we observe LMSR to converge in far fewer than n iterations when M is wellconditio”
DINGO: Distributed Newton-Type Method for Gradient-Norm Optimization (2019, methodology): “For our implementation of DINGO, we compute v (1) t,i , v (2) t,i and v (3) t,i using MINRES-QLP [24], LSMR [25] and CG, respectively, with early termination.”
Optimizing error of high-dimensional statistical queries under differential privacy (2018, methodology): “Unfortunately, we are not aware of an efficient method for computing the pseudo inverse of a strategy produced by OPT+, but we can still perform inference by using an iterative algorithm like LSMR [14] to solve the least squares problem.”