Solving Generalized Least-Squares Problems with LSQR

  • Authors:

  • Steven J. Benbow

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Matrix Analysis and Applications
  • Year:
  • 1999

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Abstract

An iterative method for solving augmented linear systems in a generalized least-squares sense is given. The method, LSQR(A-1), is shown to be a natural extension of the LSQR algorithm of Paige and Saunders [ACM Trans. Math. Software, 8 (1982), pp. 43--71], with generalized orthogonality properties so that the Cholesky factor of A is not required. Instead it is only assumed that some method of calculating the effect of (A-1) on a vector is available. Numerical experiments comparing LSQR(A-1)with similar preconditioned Krylov methods are described which demonstrate that the new method exhibits superior numerical properties when the Schur complement BTA-1B is ill conditioned.