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Zhaojun Bai and James Demmel, Using the matrix sign function to compute
invariant subspaces, SIAM J. Matrix Anal. Appl. 19 (1998), no. 1,
205-225 (electronic). MR 99c:65066
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Å. Björck and C. C. Paige, Loss and recapture of orthogonality in
the modified Gram-Schmidt algorithm, SIAM J. Matrix Anal. Appl.
13 (1992), no. 1, 176-190. MR 93c:65056
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Å. Björck, Solving linear least squares problems by
Gram-Schmidt orthogonalisation, BIT 7 (1967), 1-21.
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A. Bouras and V. Fraysse, A relaxation strategy for inexact matrix-vector
products for Krylov methods, Technical Report TR/PA/00/15, CERFACS,
France, 2000.
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A. Bouras, V. Fraysse, and L. Giraud, A relaxation strategy for
inner-outer linear solvers in domain decomposition methods, Technical Report
TR/PA/00/17, CERFACS, France, 2000.
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J.W. Daniel, W.B. Gragg, L. Kaufman, and G.W. Stewart,
Reorthogonalization and stable algorithms for updating the
Gram-Schmidt QR factorization, Math. Comp. 30 (1976),
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L. Giraud, J. Langou, M. Rozlozník, and J. van den Eshof,
Rounding error analysis of the classical Gram-Schmidt
orthogonalization process, Technical Report TR/PA/04/77, CERFACS,
Toulouse, France, 2004.
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Luc Giraud and Lucien J. Langou, Robust selective Gram-Schmidt
reorthogonalization, Technical Report TR/PA/02/52, CERFACS, Toulouse,
France, 2002, Submitted to SISC Copper Mountain Special Issue.
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to3em, When modified Gram-Schmidt generates a well-conditioned set
of vectors, IMA Journal of Numerical Analysis 22 (2002),
no. 4, 521-528.
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Luc Giraud, Langou Jucien, and Rozlozník Miro, On the round-off
error analysis of the Gram-Schmidt algorithm with reorthogonalization,
Technical Report TR/PA/02/33, CERFACS, Toulouse, France, 2002.
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Anne Greenbaum, Vlastimil Pták, and Zdenek Strakoš, Any
nonincreasing convergence curve is possible for GMRES, SIAM J.
Matrix Anal. Appl. 17 (1996), no. 3, 465-469. MR 97c:65057
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Anne Greenbaum, M. Rozlozník, and Zdenek Strakoš,
Numerical behaviour of the modified Gram-Schmidt GMRES
implementation, BIT 37 (1997), no. 3, 706-719, Direct methods,
linear algebra in optimization, iterative methods (Toulouse, 1995/1996).
MR 99a:65036
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W. Hoffmann, Iterative algorithms for Gram-Schmidt
orthogonalization, Computing 41 (1989), no. 4, 335-348.
MR 90m:65081
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C. Lanczos, An iteration method for the solution of the eigenvalue
problem of linear differential and integral operators, J. Res. Nat. Bur.
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Noël M. Nachtigal, Satish C. Reddy, and Lloyd N. Trefethen, How fast
are nonsymmetric matrix iterations?, SIAM J. Matrix Anal. Appl. 13
(1992), no. 3, 778-795, Iterative methods in numerical linear algebra
(Copper Mountain, CO, 1990). MR 93a:65039
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Axel Ruhe, Numerical aspects of Gram-Schmidt orthogonalization of
vectors, Linear Algebra Appl. 52/53 (1983), 591-601.
MR 84j:65034
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Youcef Saad and Martin H. Schultz, Conjugate gradient-like algorithms for
solving nonsymmetric linear systems, Math. Comp. 44 (1985),
no. 170, 417-424. MR 86d:65047
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Valeria Simoncini and Daniel B. Szyld, Theory of inexact Krylov
subspace methods and applications to scientific computing, SIAM J. Sci.
Comput. 25 (2003), no. 2, 454-477 (electronic) (2003).
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Gerard L. G. Sleijpen, Gram-Schmidt orthogonalisation, Personal
notes, Januari 2000.
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Jasper van den Eshof and Gerard L. G. Sleijpen, Inexact Krylov
subspace methods for linear systems, SIAM J. Matrix Anal. Appl. 26
(2004), no. 1, 125-153.
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A. van der Sluis and H. A. van der Vorst, The rate of convergence of
conjugate gradients, Numer. Math. 48 (1986), no. 5, 543-560.
MR 87h:65061
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Henk A. van der Vorst, Iterative methods for large linear systems,
Lecture notes on iterative methods, June 2002.
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to3em, Iterative Krylov methods for large linear systems, Cambridge
University Press, Cambridge, 2003, Cambridge Monographs on applied and
computational mathematics, 13.