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- Christopher C. Paige, Michael A. Saunders
- ACM Trans. Math. Softw.
- 1982

An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It isâ€¦ (More)

- Christopher C. Paige, Michael A. Saunders
- ACM Trans. Math. Softw.
- 1982

Received 4 June 1980; revised 23 September 1981, accepted 28 February 1982 This work was supported by Natural Sciences and Engineering Research Council of Canada Grant A8652, by the New Zealandâ€¦ (More)

- Alan J. Laub, Michael Heath, Christopher C. Paige, R. Ward
- 1986 25th IEEE Conference on Decision and Control
- 1986

An algorithm is presented in this paper for computing state space balancing transformations directly from a state space realization. The algorithm requires no "squaring up." Various algorithmicâ€¦ (More)

- George Miminis, Christopher C. Paige
- 1982 21st IEEE Conference on Decision and Control
- 1982

An algorithm is suggested for the computation of a linear state feedback for a multi-input system such that the matrix of the resultant closed-loop system has specified eigenvalues. The algorithm isâ€¦ (More)

- Sou-Cheng T. Choi, Christopher C. Paige, Michael A. Saunders
- SIAM J. Scientific Computing
- 2011

CG, SYMMLQ, and MINRES are KrylÃ³v subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetricâ€¦ (More)

- Christopher C. Paige, Miroslav RozloznÃk, Zdenek Strakos
- SIAM J. Matrix Analysis Applications
- 2006

The generalized minimum residual method (GMRES) [Y. Saad and M. Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856â€“869] for solving linear systems Ax = b is implemented as a sequence of leastâ€¦ (More)

- Christopher C. Paige, Zdenek Strakos
- SIAM J. Scientific Computing
- 2002

Minimum residual norm iterative methods for solving linear systems Ax = b can be viewed as, and are often implemented as, sequences of least squares problems involving Krylov subspaces of increasingâ€¦ (More)

A recursive least squares algorithm is presented for short baseline GPS positioning using both carrier phase and code measurements. We take advantage of the structure of the problem to make theâ€¦ (More)

1 I n t r o d u c t i o n . The LU factorizat ion is a basic and effective tool in numerical l inear algebra: given a real n x n mat r ix A whose first n 1 leading principal submatr ices are allâ€¦ (More)