Skip to main content

References References

[1]
  
Ed Anderson, Zhaojun Bai, James Demmel, Jack J. Dongarra, Jeremy DuCroz, Ann Greenbaum, Sven Hammarling, Alan E. McKenney, Susan Ostrouchov, and Danny Sorensen, LAPACK Users' Guide, SIAM, Philadelphia, 1992.
[2]
  
Paolo Bientinesi, Enrique S. Quintana-Orti, Robert A. van de Geijn, Representing linear algebra algorithms in code: the FLAME application program interfaces, ACM Transactions on Mathematical Software (TOMS), 2005
[3]
  
Paolo Bientinesi, Robert A. van de Geijn, Goal-Oriented and Modular Stability Analysis, SIAM Journal on Matrix Analysis and Applications , Volume 32 Issue 1, February 2011.
[4]
  
Paolo Bientinesi, Robert A. van de Geijn, The Science of Deriving Stability Analyses, FLAME Working Note #33. Aachen Institute for Computational Engineering Sciences, RWTH Aachen. TR AICES-2008-2. November 2008.
[5]
  
Christian Bischof and Charles Van Loan, The WY Representation for Products of Householder Matrices, SIAM Journal on Scientific and Statistical Computing, Vol. 8, No. 1, 1987.
[7]
  
A.K. Cline, C.B. Moler, G.W. Stewart, and J.H. Wilkinson, An estimate for the condition number of a matrix, SIAM J. Numer. Anal., 16 (1979).
[8]
  
Jack J. Dongarra, Jeremy DuCroz, Ann Greenbaum, Sven Hammarling, Alan E. McKenney, Susan Ostrouchov, and Danny Sorensen, LAPACK Users' Guide, SIAM, Philadelphia, 1992.
[9]
  
Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, and Iain Duff, A Set of Level 3 Basic Linear Algebra Subprograms, ACM Transactions on Mathematical Software, Vol. 16, No. 1, pp. 1-17, March 1990.
[10]
  
Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, and Richard J. Hanson, An Extended Set of {FORTRAN} Basic Linear Algebra Subprograms, ACM Transactions on Mathematical Software, Vol. 14, No. 1, pp. 1-17, March 1988.
[11]
  
J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart, LINPACK Users' Guide, Society for Industrial and Applied Mathematics, 1979.
[12]
  
Leslie V. Foster, Gaussian elimination with partial pivoting can fail in practice, SIAM Journal on Matrix Analysis and Applications, 15, 1994.
[13]
  
Gene H. Golub and Charles F. Van Loan, Matrix Computations, Fourth Edition, Johns Hopkins Press, 2013.
[14]
  
Brian C. Gunter, Robert A. van de Geijn, Parallel out-of-core computation and updating of the QR factorization, ACM Transactions on Mathematical Software (TOMS), 2005.
[15]
  
N. Higham, A Survey of Condition Number Estimates for Triangular Matrices, SIAM Review, 1987.
[16]
  
C. G. J. Jacobi, Über ein leichtes Verfahren, die in der Theorie der Sä kular-störungen vorkommenden Gleichungen numerisch aufzulösen, Crelle's Journal 30, 51-94, 1846.
[17]
  
Thierry Joffrain, Tze Meng Low, Enrique S. Quintana-Orti, Robert van de Geijn, Field G. Van Zee, Accumulating {H}ouseholder transformations, revisited, ACM Transactions on Mathematical Software, Vol. 32, No 2, 2006.
[18]
  
C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software, Vol. 5, No. 3, pp. 308-323, Sept. 1979.
[19]
  
Per-Gunnar Martinsson, Gregorio Quintana-Orti, Nathan Heavner, Robert van de Geijn, Householder QR Factorization With Randomization for Column Pivoting (HQRRP), SIAM Journal on Scientific Computing, Vol. 39, Issue 2, 2017.
[20]
  
Margaret E. Myers, Pierce M. van de Geijn, and Robert A. van de Geijn, Linear Algebra: Foundations to Frontiers - Notes to LAFF With, self-published at ulaff.net, 2014.
[21]
  
Margaret E. Myers and Robert A. van de Geijn, Linear Algebra: Foundations to Frontiers, a Massive Open Online Course offered on edX.
[22]
  
J. Novembre, T. Johnson, K. Bryc, Z. Kutalik, A.R. Boyko, A. Auton, A. Indap, K.S. King, S. Bergmann, M.. Nelson, M. Stephens, C.D. Bustamante, Genes mirror geography within Europe, Nature, 2008
[23]
  
C. Puglisi, Modification of the Householder method based on the compact WY representation, SIAM Journal on Scientific Computing, Vol. 13, 1992.
[24]
  
Gregorio Quintana-Orti, Xioabai Sun, and Christof H. Bischof, A BLAS-3 version of the QR factorization with column pivoting, SIAM Journal on Scientific Computing, 19, 1998.
[25]
  
Robert Schreiber and Charles Van Loan, A Storage-Efficient WY Representation for Products of Householder Transformations, SIAM Journal on Scientific and Statistical Computing, Vol. 10, No. 1, 1989.
[26]
  
G.W. Stewart, Matrix Algorithms, Volume I: Basic Decompositions, SIAM Press, 2001.
[27]
  
Robert van de Geijn and Kazushige Goto, BLAS (Basic Linear Algebra Subprograms), Encyclopedia of Parallel Computing, Part 2, pp. 157-164, 2011. If you don't have access, you may want to read an advanced draft.
[28]
  
Field G. Van Zee, Robert A. van de Geijn, Gregorio Quintana-Ortí, Restructuring the Tridiagonal and Bidiagonal QR Algorithms for Performance, ACM Transactions on Mathematical Software (TOMS), Vol. 40, No. 3, 2014.

Available free from http://www.cs.utexas.edu/~flame/web/FLAMEPublications.html Journal Publication #33. Click on the title of the paper.

[29]
  
Field G. Van Zee, Robert A. van de Geijn, Gregorio Quintana-Ortí, G. Joseph Elizondo, Families of Algorithms for Reducing a Matrix to Condensed Form. ACM Transactions on Mathematical Software (TOMS) , Vol, No. 1, 2012.

Available free from http://www.cs.utexas.edu/~flame/web/FLAMEPublications.html Journal Publication #26. Click on the title of the paper.

[30]
  
H. F. Walker, Implementation of the GMRES method using Householder transformations, SIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 1, 1988.
[31]
  
Stephen J. Wright, A Collection of Problems for Which {G}aussian Elimination with Partial Pivoting is Unstable, SIAM Journal on Scientific Computing, Vol. 14, No. 1, 1993.
[32]
  
Margaret E. Myers and Robert A. van de Geijn, LAFF-On Programming for Correctness, ulaff.net, 2017.