Accession Number:

ADA063334

Title:

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

Descriptive Note:

Technical rept.,

Corporate Author:

STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB

Report Date:

1978-10-01

Pagination or Media Count:

95.0

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

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE