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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]
  
Richard Barrett, Michael Berry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM Press, 1993. [ PDF ]
[3]
  
Paolo Bientinesi, Inderjit S. Dhillon, Robert A. van de Geijn, A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations, SIAM Journal on Scientific Computing, 2005
[4]
  
Paolo Bientinesi, John A. Gunnels, Margaret E. Myers, Enrique S. Quintana-Orti, Robert A. van de Geijn, The science of deriving dense linear algebra algorithms, ACM Transactions on Mathematical Software (TOMS), 2005.
[5]
  
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
[6]
  
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.
[7]
  
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 200x8.
[8]
  
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.
[9]
  
Basic Linear Algebra Subprograms - A Quick Reference Guide, University of Tennessee, Oak Ridge National Laboratory, Numerical Algorithms Groiup Ltd.
[11]
  
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).
[12]
  
Inderjit S. Dhillon and Beresford N. Parlett, Multiple Representations to Compute Orthogonal Eigenvectors of Symmetric Tridiagonal Matrices, Lin. Alg. Appl., Vol. 387, 2004.
[13]
  
Jack J. Dongarra, Jeremy DuCroz, Ann Greenbaum, Sven Hammarling, Alan E. McKenney, Susan Ostrouchov, and Danny Sorensen, LAPACK Users' Guide, SIAM, Philadelphia, 1992.
[14]
  
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.
[15]
  
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.
[16]
  
J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart, LINPACK Users' Guide, Society for Industrial and Applied Mathematics, 1979.
[18]
  
Leslie V. Foster, Gaussian elimination with partial pivoting can fail in practice, SIAM Journal on Matrix Analysis and Applications, 15, 1994.
[19]
  
Gene H. Golub and Charles F. Van Loan, Matrix Computations, Fourth Edition, Johns Hopkins Press, 2013.
[20]
  
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.
[21]
  
N. Higham, A Survey of Condition Number Estimates for Triangular Matrices, SIAM Review, 1987.
[22]
  
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.
[23]
  
Thierry Joffrain, Tze Meng Low, Enrique S. Quintana-Orti, Robert van de Geijn, Field G. Van Zee, Accumulating Householder transformations, revisited, ACM Transactions on Mathematical Software, Vol. 32, No 2, 2006.
[24]
  
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.
[25]
  
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.
[26]
  
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.
[27]
  
Margaret E. Myers and Robert A. van de Geijn, Linear Algebra: Foundations to Frontiers, ulaff.net, 2014. A Massive Open Online Course offered on edX.
[28]
  
Margaret E. Myers and Robert A. van de Geijn, LAFF-On Programming for Correctness, self-published at ulaff.net, 2017.
[29]
  
Margaret E. Myers and Robert A. van de Geijn, LAFF-On Programming for Correctness, A Massive Open Online Course offered on edX.
[30]
  
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
[31]
  
Devangi N. Parikh, Margaret E. Myers, Richard Vuduc, Robert A. van de Geijn, A Simple Methodology for Computing Families of Algorithms, FLAME Working Note #87, The University of Texas at Austin, Department of Computer Science, Technical Report TR-18-06. arXiv:1808.07832.
[32]
  
C. Puglisi, Modification of the Householder method based on the compact WY representation, SIAM Journal on Scientific Computing, Vol. 13, 1992.
[33]
  
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.
[34]
  
Martin D. Schatz, Robert A. van de Geijn, and Jack Poulson, Parallel Matrix Multiplication: A Systematic Journey, SIAM Journal on Scientific Computing, Volume 38, Issue 6, 2016.
[35]
  
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.
[36]
  
Jonathon Shlens, A Tutorial on Principal Component Analysis, arxiv 1404.1100, 2014.
[37]
  
G.W. Stewart, Matrix Algorithms, Volume I: Basic Decompositions, SIAM Press, 2001.
[38]
  
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.
[40]
  
Robert van de Geijn, Margaret Myers, and Devangi N. Parikh, LAFF-On Programming for High Performance, ulaff.net, 2019.
[41]
  
Robert van de Geijn, Margaret Myers, and Devangi N. Parikh, LAFF-On Programming for High Performance, A Massive Open Online Course offered on edX.
[42]
  
Robert van de Geijn and Jerrell Watts, SUMMA: Scalable Universal Matrix Multiplication Algorithm, Concurrency: Practice and Experience, Volume 9, Number 4, 1997.
[44]
  
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.

[45]
  
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.

[46]
  
H. F. Walker, Implementation of the GMRES method using Householder transformations, SIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 1, 1988.
[47]
  
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.
[50]
  
Kazushige Goto and Robert van de Geijn, Anatomy of High-Performance Matrix Multiplication, ACM Transactions on Mathematical Software, Vol. 34, No. 3: Article 12, May 2008.
[51]
  
Tyler Michael Smith, Bradley Lowery, Julien Langou, Robert A. van de Geijn, A Tight I/O Lower Bound for Matrix Multiplication, arxiv.org:1702.02017v2, 2019. (To appear in ACM Transactions on Mathematical Software.)
[52]
  
Field G. Van Zee and Tyler M. Smith, Implementing High-performance Complex Matrix Multiplication via the 3M and 4M Methods, ACM Transactions on Mathematical Software, Vol. 44, No. 1, pp. 7:1-7:36, July 2017.
[53]
  
Field G. Van Zee and Robert A. van de Geijn, BLIS: A Framework for Rapidly Instantiating BLAS Functionality, ACM Journal on Mathematical Software, Vol. 41, No. 3, June 2015. You can access this article for free by visiting the Science of High-Performance Computing group webpage and clicking on the title of Journal Article 39.