Solving Generalized Least-Squares Problems with LSQR
Steven J. Benbow · SIAM Journal on Matrix Analysis and Applications · 1999
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 B T A -1 B is ill conditioned.