Some publications and talks, some for downloading. Partially updated 9 March 2019
[Pai19] C. C. Paige.
Accuracy of the Lanczos process for the eigenproblem and solution of equations.
-- .pdf file.
Submitted to SIAM Journal on Matrix Analysis and Applications (SIMAX),
June 2017.
[Pai18] C. C. Paige.
The Effects of Loss of Orthogonality on Large Scale Numerical Computations.
In: O. Gervasi et al. (Eds.):
Computational Science and Its Applications, ICCSA (2018), pp. 429--439.
Lecture Notes in Computer Science, vol 10962. Springer, Cham.
https://doi.org/10.1007/978-3-319-95168-3_29
[GrePTV16] C. Greif, C. C. Paige, D. Titley-Peloquin, & J. M. Varah.
Numerical equivalences among Krylov subspace algorithms for skew-symmetric matrices.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX),
37:1071--1087, 2016. (Open access).
https://doi.org/10.1137/15M1030078
[PaiW14] C. C. Paige and W. Wuelling.
Properties of a unitary matrix obtained from a sequence of normalized vectors.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX),
35:526--545, 2014.
https://doi.org/10.1137/120897687
[PaiPZ13] C. C. Paige, I. Panayotov, & J.-P. M. Zemke.
An augmented analysis of the perturbed two-sided Lanczos tridiagonalization process.
Linear Algebra Appl., 447:119--132, 2014.
https://doi.org/10.1016/j.laa.2013.05.009
[ChoPS11] S.-C. T. Choi, C. C. Paige, and M. A. Saunders.
MINRES-QLP: A Krylov subspace method for indefinite or singular symmetric systems.
SIAM Journal on Scientific Computing, 33(4):1810--1836, 2011.
https://doi.org/10.1137/100787921
[PaiP11] C. C. Paige & I. Panayotov.
Hessenberg matrix properties and Ritz vectors in the
finite-precision Lanczos tridiagonalization process.
SIAM Journal on Matrix Analysis and Applications (SIMAX), 32:1079--1094, 2011.
https://doi.org/10.1137/100796285
[Pai10] C. C. Paige.
An augmented stability result for the Lanczos Hermitian matrix tridiagonalization process.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX), 31:2347--2359, 2010.
https://doi.org/10.1137/090761343
[Pai09] C. C. Paige.
A useful form of unitary matrix obtained from any sequence of unit 2-norm N-vectors.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX), 31:565--583, 2009.
https://doi.org/10.1137/080725167
[ChaPTP09] X.-W. Chang, C. C. Paige, & D. Titley-Peloquin.
Stopping criteria for the iterative solution of linear least squares problems.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX), 31:831--852, 2009.
[ChaPT08] X.-W. Chang, C. C. Paige, & D. Titley-Peloquin.
Characterizing matrices that are consistent with given solutions.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX),
30:1406--1420, 2008.
[ChaGP09] X.-W. Chang, G. H. Golub, & C. C. Paige.
Towards a backward perturbation analysis for data least squares problems.
-- .pdf file.
SIAM Journal on Matrix Analysis and Applications (SIMAX),
30:1281--1301, 2008.
[PaiP08] C. C. Paige & I. Panayotov.
Majorization bounds for ritz values of hermitian matrices.
-- .pdf file.
Electronic Transactions on Numerical Analysis (ETNA), 31:1--11, 2008.
[ArgKPP08] M. E. Argentati, A. V. Knyazev, C. C. Paige, & I. Panayotov.
Bounds on changes in Ritz values for a perturbed invariant subspace
of a Hermitian matrix.
SIAM Journal on Matrix Analysis and Applications (SIMAX), 30(2):548--559, 2008.
Also published as a technical report
http://arxiv.org/abs/math/0610498
[PaiSWZ08] C. C. Paige, G.P.H. Styan, B.-Y. Wang, & F. Zhang.
Hua's matrix equality and Schur complements.
-- .pdf file.
International Journal of Information and System Sciences, 4:124--135, 2008.
[ChaP07] X.-W. Chang & C. C. Paige.
Euclidean distances and least squares problems for a given set of vectors.
-- .pdf file.
Applied Numerical Mathematics, 57:1240--1244, 2007.
[PaiRS06] C. C. Paige, M. Rozloznik, & Z. Strakos.
Modified Gram-Schmidt (MGS), least squares, and backward stability of MGS-GMRES
-- .pdf file.
SIAM J. Matrix Anal. Appl., 28:264--284, 2006.
https://doi.org/10.1137/050630416
Talk -- .pdf file,
at the 16th Householder Symposium on
Numerical Linear Algebra, Pennsylvania, May 22-27, 2005.
[PaiS06] C. C. Paige & Z. Strakos.
Core problems in linear algebraic systems -- .pdf file,
.ps file.
SIAM J. Matrix Anal. Appl., 27:861--875, 2006.
Talk -- .pdf file,
at the 16th Householder Symposium on
Numerical Linear Algebra, Pennsylvania, May 22-27, 2005.
[ChaPT05] X.-W. Chang, C. C. Paige, & C. C. J. M. Tiberius.
Computation of a test statistic in data quality control -- .pdf file.
SIAM Journal on Scientific Computing, 26:1916--1931, 2005.
Talk -- .pdf file,
at the ERCIM WG Matrix Computations and Statistics workshop,
Prague, August 27-29, 2004.
[ChaPY04] X.-W. Chang, C. C. Paige, & L. Yin.
Code and carrier phase based short baseline GPS positioning:
Computational aspects -- .pdf file.
GPS Solutions, 7:230--240, 2004.
[ChaP03a] X.-W. Chang & C. C. Paige.
An orthogonal transformation algorithm for GPS positioning -- .pdf file.
SIAM Journal on Scientific Computing, 24:1710--1732, 2003.
The original SIAM publication is available here.
[ChaP03b] X.-W. Chang & C. C. Paige.
An algorithm for combined code and carrier phase based GPS positioning
-- .pdf file.
BIT Numerical Mathematics, 43:915--927, 2003.
[MonPS03] P. Montagnier, C. C. Paige, & R. J. Spiteri.
Real Floquet factors of linear time-periodic systems -- .pdf file.
Systems & Control Letters, 50:251--262, November 2003.
The original Elsevier publication is available here.
[ChaP02] X.-W. Chang & C. C. Paige.
Numerical linear algebra in the integrity theory of the global positioning system
-- .pdf file.
Computational Statistics and Data Analysis, 41:123--142, 2002.
[PaiS02b] C. C. Paige & Z. Strakos.
Scaled Total Least Squares Fundamentals -- .pdf file. (Copyright Springer-Verlag.)
Numerische Mathematik 91:117--146, 2002.
https://doi.org/10.1007/s002110100314
[PaiS02c] C. C. Paige & Z. Strakos.
Residual and backward error bounds in minimum residual Krylov subspace methods
-- .pdf file.
.
SIAM J. Sci. Comput., 23:1898--1923, 2002.
The original SIAM electronic publication is available here.
[PaiS02a] C. C. Paige & Z. Strakos.
Bounds for the Least Squares Distance using Scaled Total Least Squares
-- .pdf file.
(Copyright Springer-Verlag.)
Numerische Mathematik, 91:93--115, 2002.
[PaiS02d] C. C. Paige & Z. Strakos.
Unifying least squares, total least squares and data least squares -- .pdf file.
In S. van Huffel & P. Lemmerling, editors, ``Total Least Squares
and Errors-in-Variables Modeling'', pages 25--34.
Kluwer Academic Publishers, Dordrecht, 2002.
[PaiS02e] C. C. Paige & Z. Strakos.
Bounds for the least squares residual using scaled Total Least Squares
-- .pdf file.
In S. van Huffel & P. Lemmerling, editors, ``Total Least Squares
and Errors-in-Variables Modeling'', pages 35--44.
Kluwer Academic Publishers, Dordrecht, 2002.
[ChaP01] X.-W. Chang & C. C. Paige.
Componentwise Perturbation Analyses for the QR Factorization -- .pdf file.
Numerische Mathematik, 88:319--345, 2001.
[PaiVD99] C. C. Paige & P. Van Dooren.
Sensitivity Analysis of the Lanczos Reduction -- .pdf file.
Numerical Linear Algebra with Applications, 6:29--50, 1999.
[ChaP98a] X.-W. Chang & C. C. Paige.
Perturbation Analyses for the Cholesky Downdating Problem -- .ps file.
SIAM J. Matrix Anal. Appl., 19:429--443, 1998.
[ChaP98b] X.-W. Chang & C. C. Paige.
On the Sensitivity of the LU Factorization -- .ps file.
BIT, 38:486--501, 1998.
[ChaP98c] X.-W. Chang & C. C. Paige.
Sensitivity Analyses for Factorizations of Sparse or Structured Matrices
-- .ps file.
Linear Algebra and Appl., 284:53--71, 1998.
[ChaPS97] X.-W. Chang, C. C. Paige & G. W. Stewart.
Perturbation Analyses for the QR Factorization -- .ps file.
SIAM J. Matrix Anal. Appl., 18:775--791, 1997.
[ChaPS96] X.-W. Chang, C. C. Paige & G. W. Stewart.
New Perturbation Analyses for the Cholesky Factorization -- .ps file.
IMA J. Numer. Anal., 16:457--484, 1996.
[PaiPV95] C. C. Paige, B. N. Parlett & H. A. van der Vorst.
Approximate Solutions and Eigenvalue Bounds from Krylov Subspaces -- .ps file.
Numerical Linear Algebra with Applications, 2:115--133, 1995.
[PaiW94] C. C. Paige & M. Wei.
History and Generality of the CS Decomposition -- .ps file.
Linear Algebra and Appl., 208/209:303--326, 1994.
[BjoP94] A. Bjorck & C. C. Paige.
Solution of Augmented Linear Systems using Orthogonal Factorizations
-- .ps file.
BIT Numerical Mathematics, 34:1--24, 1994.
[BjoP92] A. Bjorck & C. C. Paige.
Loss and Recapture of Orthogonality in the Modified Gram-Schmidt Algorithm
-- .ps file.
SIAM J. Matrix Anal. Appl., 13:176--190, 1992.
https://doi.org/10.1137/0613015
[Pai85] C. C. Paige.
Covariance matrix representation in linear filtering -- .ps file.
In "Linear Algebra and Its Role in Systems Theory", B.N. Datta Ed., AMS Publns., Providence RI, 1985, pp. 309--321.