LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

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Abstract

An iterative method is given for solving Ax ~ffi b and minU Ax -b 112, 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.

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Authors

Christopher C. Paige

McGill University

Michael A. Saunders

Tecplot (United States)

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ACM Transactions on Mathematical Software

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Stanford University

McGill University

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Paige et al. (Mon,) studied this question.

synapsesocial.com/papers/6a026b3c409fa9622d51273a — DOI: https://doi.org/10.1145/355984.355989

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Bidiagonalization of Matrices and Solution of Linear Equations· 1974 · 115 citations
Methods of conjugate gradients for solving linear systems· 1952 · 8,026 citations
Computational Methods of Linear Algebra· 1964 · 1,611 citations
Iterative methods for linear least squares problems.· 1974 · 34 citations
The Algebraic Eigenvalue Problem· 1966 · 5,224 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bidiagonalization of Matrices and Solution of Linear Equations· 1974 · 115 citations
Methods of conjugate gradients for solving linear systems· 1952 · 8,026 citations
Computational Methods of Linear Algebra· 1964 · 1,611 citations
Iterative methods for linear least squares problems.· 1974 · 34 citations
The Algebraic Eigenvalue Problem· 1966 · 5,224 citations

LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

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