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LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares (1982)
| Venue: | ACM Trans. Math. Software |
| Citations: | 644 - 21 self |
BibTeX
@ARTICLE{Paige82lsqr:an,
author = {Christopher C. Paige and Michael A. Saunders},
title = {LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares},
journal = {ACM Trans. Math. Software},
year = {1982},
pages = {43--71}
}
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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. 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 I~QR with several other conjugate-gradient algorithms, indicating that I~QR is the most reliable algorithm when A is ill-conditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmation--least squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and
Keyphrases
sparse linear equation sparse least square numerical analysis standard error ax ffi subroutine lsqr iterative method reliable algorithm conjugate gradient standard method subject descriptor numerical linear algebra linear system numerical test several conjugate-gradient algorithm condition number fortran implementation favorable numerical property bidiagonalization procedure minu ax
