A Bidiagonalization Algorithm for Sparse Linear Equations and Least-Squares Problems.

Abstract

A method is given for solving Ax = b and min value of (Ax-b) sub 2 where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytical equivalent to the method of conjugate gradients (CG) but possesses more favorable numerical properties. The Fortran implementation of the method (subroutine LSQR) incorporates reliable stopping criteria and provides estimates of various quantities including standard errors for x and the condition number of A. Numerical tests are described comparing LSQR with several other CG algorithms. Further results for a large practical problem illustrate the effect of pre-conditioning least-squares problems using a sparse LU factorization of A. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1978
Accession Number
ADA063334

Entities

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  • Christopher C. Paige
  • Michael Saunders

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  • Stanford University

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  • Algorithms
  • Analysis Of Variance
  • Applied Mathematics
  • Arithmetic
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  • Differential Equations
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