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.