论文信息 - Solving Generalized Least-Squares Problems with LSQR

Solving Generalized Least-Squares Problems with LSQR

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.

Steven J. Benbow | S. Benbow

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