Some publications and recent talks for downloading. Updated 1 Sep. 08

  • [Pai09] C.C. Paige. A useful form of unitary matrix obtained from any sequence of unit 2-norm N-vectors. SIAM Journal on Matrix Analysis and Applications (SIMAX). Submitted for publication May 2008. -- .pdf file of a talk based on this.
  • [ChaPT09] 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), 2008. Accepted for publication May 27, 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), 2008. Accepted for publication March 31, 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.
  • [PaiRSTalkNRBE06] C.C. Paige, M. Rozloznik, & Z. Strakos. Talk on stopping criteria for solving large linear systems -- .pdf file, -- .ps file, given at The International Conference on Adaptivity and Beyond: Computational Methods for Solving Differential Equations. Vancouver, August 3-6, 2005.
  • [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. 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.
  • [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. (This is mostly an easy introduction to some of the ideas in [PaiS02b]).
  • [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.
  • [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.