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Software for Numerical Linear Algebra

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Matrix Algebra

Part of the book series: Springer Texts in Statistics ((STS))

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Abstract

There is a variety of computer software available to perform the operations on vectors and matrices discussed in Chap. 11 and previous chapters. We can distinguish software based on various dimensions, including the kinds of applications that the software emphasizes, the level of the objects it works with directly, and whether or not it is interactive. We can also distinguish software based on who “owns” the software and its availability to other users. Many commercial software systems are available from the developers/owners through licensing agreements, and the rights of the user are restricted by the terms of the license, in addition to any copyright.

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References

  • Anderson, E., Z. Bai, C. Bischof, L. S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenhaum, S. Hammarling, A. McKenney, and D. Sorensen. 2000. LAPACK Users’ Guide, 3rd ed. Philadelphia: Society for Industrial and Applied Mathematics.

    MATH  Google Scholar 

  • ANSI. 1978. American National Standard for Information Systems — Programming Language FORTRAN, Document X3.9-1978. New York: American National Standards Institute.

    Google Scholar 

  • ANSI. 1992. American National Standard for Information Systems — Programming Language Fortran-90, Document X3.9-1992. New York: American National Standards Institute.

    Google Scholar 

  • Attaway, Stormy. 2016. Matlab: A Practical Introduction to Programming and Problem Solving, 4th ed. Oxford, United Kingdom: Butterworth-Heinemann.

    Google Scholar 

  • Barker, V. A., L. S. Blackford, J. Dongarra, J. Du Croz, S. Hammarling, M. Marinova, J. Wasniewsk, and P. Yalamov. 2001. LAPACK95 Users’ Guide. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Barrett, R., M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst. 1994. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Birkhoff, Garrett, and Surender Gulati. 1979. Isotropic distributions of test matrices. Journal of Applied Mathematics and Physics (ZAMP) 30:148–158.

    Article  MathSciNet  MATH  Google Scholar 

  • Blackford, L. S., A. Cleary, A. Petitet, R. C. Whaley, J. Demmel, I. Dhillon, H. Ren, K. Stanley, J. Dongarra, and S. Hammarling. 1997b. Practical experience in the numerical dangers of heterogeneous computing. ACM Transactions on Mathematical Software 23:133–147.

    Google Scholar 

  • Blackford, L. Susan, Antoine Petitet, Roldan Pozo, Karin Remington, R. Clint Whaley, James Demmel, Jack Dongarra, Iain Duff, Sven Hammarling, Greg Henry, Michael Heroux, Linda Kaufman, and Andrew Lumsdaine. 2002. An updated set of basic linear algebra subprograms (BLAS). ACM Transactions on Mathematical Software 28:135–151.

    Article  MathSciNet  Google Scholar 

  • Buttari, Alfredo, Julien Langou, Jakub Kurzak, and Jack Dongarra. 2009. A class of parallel tiled linear algebra algorithms for multicore architectures. Parallel Computing 35:38–53.

    Article  MathSciNet  Google Scholar 

  • Chambers, John M. 2016. Extending R. Boca Raton: Chapman and Hall/CRC Press.

    MATH  Google Scholar 

  • Chapman, Barbara, Gabriele Jost, and Ruud van der Pas. 2007. Using OpenMP: Portable Shared Memory Parallel Programming. Cambridge, Massachusetts: The MIT Press.

    Google Scholar 

  • Cheng, John, Max Grossman, and Ty McKercher. 2014. Professional CUDA C Programming. New York: Wrox Press, an imprint of John Wiley and Sons.

    Google Scholar 

  • Clerman, Norman, and Walter Spector. 2012. Modern Fortran. Cambridge, United Kingdom: Cambridge University Press.

    Google Scholar 

  • Coleman, Thomas F., and Charles Van Loan. 1988. Handbook for Matrix Computations. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Dauger, Dean E., and Viktor K. Decyk. 2005. Plug-and-play cluster computing: High-performance computing for the mainstream. Computing in Science and Engineering 07(2):27–33.

    Article  MATH  Google Scholar 

  • Dongarra, J. J., J. R. Bunch, C. B. Moler, and G. W. Stewart. 1979. LINPACK Users’ Guide. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Dongarra, J. J., J. DuCroz, S. Hammarling, and I. Duff. 1990. A set of level 3 basic linear algebra subprograms. ACM Transactions on Mathematical Software 16:1–17.

    Article  MATH  Google Scholar 

  • Dongarra, J. J., J. DuCroz, S. Hammarling, and R. J. Hanson. 1988. An extended set of Fortran basic linear algebra subprograms. ACM Transactions on Mathematical Software 14:1–17.

    Article  MATH  Google Scholar 

  • Dongarra, Jack J., and Victor Eijkhout. 2000. Numerical linear algebra algorithms and software. Journal of Computational and Applied Mathematics 123:489–514.

    Article  MathSciNet  MATH  Google Scholar 

  • Duff, Iain S., Michael A. Heroux, and Roldan Pozo. 2002. An overview of the sparse basic linear algebra subprograms: the new standard from the BLAS technical forum. ACM Transactions on Mathematical Software 28:239–267.

    Article  MathSciNet  MATH  Google Scholar 

  • Duff, Iain S., Michele Marrone, Guideppe Radicati, and Carlo Vittoli. 1997. Level 3 basic linear algebra subprograms for sparse matrices: A user-level interface. ACM Transactions on Mathematical Software 23:379–401.

    Article  MathSciNet  MATH  Google Scholar 

  • Duff, Iain S., and Christof Vömel. 2002. Algorithm 818: A reference model implementation of the sparse BLAS in Fortran 95. ACM Transactions on Mathematical Software 28:268–283.

    Article  MathSciNet  MATH  Google Scholar 

  • Eddelbuettel, Dirk. 2013. Seamless R and C++ Integration with Rcpp. New York: Springer-Verlag.

    Book  MATH  Google Scholar 

  • Ericksen, Wilhelm S. 1985. Inverse pairs of test matrices. ACM Transactions on Mathematical Software 11:302–304.

    Article  MathSciNet  MATH  Google Scholar 

  • Eubank, Randall L., and Ana Kupresanin. 2012. Statistical Computing in C++ and R. Boca Raton: Chapman and Hall/CRC Press.

    MATH  Google Scholar 

  • Filippone, Salvatore, and Michele Colajanni. 2000. PSBLAS: A library for parallel linear algebra computation on sparse matrices. ACM Transactions on Mathematical Software 26:527–550.

    Article  MATH  Google Scholar 

  • Galassi, Mark, Jim Davies, James Theiler, Brian Gough, Gerard Jungman, Michael Booth, and Fabrice Rossi. 2002. GNU Scientific Library Reference Manual, 2nd ed. Bristol, United Kingdom: Network Theory Limited.

    Google Scholar 

  • Gandrud, Christopher. 2015. Reproducible Research with R and R Studio, 2nd ed. Boca Raton: Chapman and Hall/CRC Press.

    MATH  Google Scholar 

  • Geist, Al, Adam Beguelin, Jack Dongarra, Weicheng Jiang, Robert Manchek, and Vaidy Sunderam. 1994. PVM. Parallel Virtual Machine. A Users’ Guide and Tutorial for Networked Parallel Computing. Cambridge, Massachusetts: The MIT Press.

    MATH  Google Scholar 

  • Gregory, Robert T., and David L. Karney. 1969. A Collection of Matrices for Testing Computational Algorithms. New York: John Wiley and Sons.

    MATH  Google Scholar 

  • Gropp, William, Ewing Lusk, and Anthony Skjellum. 2014. Using MPI: Portable Parallel Programming with the Message-Passing Interface, 3rd ed. Cambridge, Massachusetts: The MIT Press.

    MATH  Google Scholar 

  • Gropp, William, Ewing Lusk, and Thomas Sterling (Editors). 2003. Beowulf Cluster Computing with Linux, 2nd ed. Cambridge, Massachusetts: The MIT Press.

    Google Scholar 

  • Hanson, Richard J., and Tim Hopkins. 2013. Numerical Computing with Modern Fortran. Philadelphia: Society for Industrial and Applied Mathematics.

    MATH  Google Scholar 

  • Heroux, Michael A. 2015. Editorial: ACM TOMS replicated computational results initiative. ACM Transactions on Mathematical Software 41:Article No. 13.

    Google Scholar 

  • Higham, Nicholas J. 1991. Algorithm 694: A collection of test matrices in Matlab. ACM Transactions on Mathematical Software 17:289–305.

    Article  MATH  Google Scholar 

  • Higham, Nicholas J. 2002. Accuracy and Stability of Numerical Algorithms, 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics.

    Book  MATH  Google Scholar 

  • Karau, Holden, Andy Konwinski, Patrick Wendell, and Matei Zaharia. 2015. Learning Spark. Sabastopol, California: O’Reilly Media, Inc.

    Google Scholar 

  • Lawson, C. L., R. J. Hanson, D. R. Kincaid, and F. T. Krogh. 1979. Basic linear algebra subprograms for Fortran usage. ACM Transactions on Mathematical Software 5:308–323.

    Article  MATH  Google Scholar 

  • Lemmon, David R., and Joseph L. Schafer. 2005. Developing Statistical Software in Fortran 95. New York: Springer-Verlag.

    MATH  Google Scholar 

  • Markus, Arjen. 2012. Modern Fortran in Practice. Cambridge, United Kingdom: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Metcalf, Michael, John Reid, and Malcolm Cohen. 2011. Modern Fortran Explained. Oxford, United Kingdom: Oxford University Press.

    MATH  Google Scholar 

  • Nakano, Junji. 2012. Parallel computing techniques. In Handbook of Computational Statistics: Concepts and Methods, 2nd revised and updated ed., ed. James E. Gentle, Wolfgang Härdle, and Yuichi Mori, 243–272. Berlin: Springer.

    Chapter  Google Scholar 

  • Quinn, Michael J. 2003. Parallel Programming in C with MPI and OpenMP. New York: McGraw-Hill.

    Google Scholar 

  • Rice, John R. 1993. Numerical Methods, Software, and Analysis, 2nd ed. New York: McGraw-Hill Book Company.

    MATH  Google Scholar 

  • Roosta, Seyed H. 2000. Parallel Processing and Parallel Algorithms: Theory and Computation. New York: Springer-Verlag.

    Book  MATH  Google Scholar 

  • Siek, Jeremy, and Andrew Lumsdaine. 2000. A modern framework for portable high-performance numerical linear algebra. In Advances in Software Tools for Scientific Computing, ed. Are Bruaset, H. Langtangen, and E. Quak, 1–56. New York: Springer-Verlag.

    Google Scholar 

  • Smith, B. T., J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler. 1976. Matrix Eigensystem Routines — EISPACK Guide. Berlin: Springer-Verlag.

    Book  MATH  Google Scholar 

  • Stodden, Victoria, Friedrich Leisch, and Roger D. Peng. 2014. Implementing Reproducible Research. Boca Raton: Chapman and Hall/CRC Press.

    Google Scholar 

  • Venables, W. N., and B. D. Ripley. 2003. Modern Applied Statistics with S, 4th ed. New York: Springer-Verlag.

    MATH  Google Scholar 

  • White, Tom. 2015. Hadoop: The Definitive Guide, 4th ed. Sabastopol, California: O’Reilly Media, Inc.

    Google Scholar 

  • Wickham, Hadley. 2015) Advanced R. Boca Raton: Chapman and Hall/CRC Press.

    Google Scholar 

  • Xie, Yihui. 2015. Dynamic Documents with R and knitr, 2nd ed. Boca Raton: Chapman and Hall/CRC Press.

    Google Scholar 

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Authors and Affiliations

  1. Fairfax, VA, USA

    James E. Gentle

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  1. James E. Gentle
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Gentle, J.E. (2017). Software for Numerical Linear Algebra. In: Matrix Algebra. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-64867-5_12

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