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Matrix Algebra pp 539-585 | Cite as

Software for Numerical Linear Algebra

  • James E. Gentle
Chapter
  • 5.9k Downloads
Part of the Springer Texts in Statistics book series (STS)

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.

Keywords

Automatically Tuned Linear Algebra Software (ATLAS) Comprehensive R Archive Network (CRAN) Modern Fortran Guide To Available Mathematical Software (GAMS) Coarray 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 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.zbMATHGoogle Scholar
  2. ANSI. 1978. American National Standard for Information Systems — Programming Language FORTRAN, Document X3.9-1978. New York: American National Standards Institute.Google Scholar
  3. ANSI. 1992. American National Standard for Information Systems — Programming Language Fortran-90, Document X3.9-1992. New York: American National Standards Institute.Google Scholar
  4. Attaway, Stormy. 2016. Matlab: A Practical Introduction to Programming and Problem Solving, 4th ed. Oxford, United Kingdom: Butterworth-Heinemann.Google Scholar
  5. 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.CrossRefzbMATHGoogle Scholar
  6. 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.CrossRefzbMATHGoogle Scholar
  7. Birkhoff, Garrett, and Surender Gulati. 1979. Isotropic distributions of test matrices. Journal of Applied Mathematics and Physics (ZAMP) 30:148–158.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 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
  9. 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.MathSciNetCrossRefGoogle Scholar
  10. 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.MathSciNetCrossRefGoogle Scholar
  11. Chambers, John M. 2016. Extending R. Boca Raton: Chapman and Hall/CRC Press.zbMATHGoogle Scholar
  12. Chapman, Barbara, Gabriele Jost, and Ruud van der Pas. 2007. Using OpenMP: Portable Shared Memory Parallel Programming. Cambridge, Massachusetts: The MIT Press.Google Scholar
  13. 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
  14. Clerman, Norman, and Walter Spector. 2012. Modern Fortran. Cambridge, United Kingdom: Cambridge University Press.Google Scholar
  15. Coleman, Thomas F., and Charles Van Loan. 1988. Handbook for Matrix Computations. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefzbMATHGoogle Scholar
  16. 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.CrossRefzbMATHGoogle Scholar
  17. Dongarra, J. J., J. R. Bunch, C. B. Moler, and G. W. Stewart. 1979. LINPACK Users’ Guide. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefzbMATHGoogle Scholar
  18. 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.CrossRefzbMATHGoogle Scholar
  19. 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.CrossRefzbMATHGoogle Scholar
  20. Dongarra, Jack J., and Victor Eijkhout. 2000. Numerical linear algebra algorithms and software. Journal of Computational and Applied Mathematics 123:489–514.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 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.MathSciNetCrossRefzbMATHGoogle Scholar
  24. Eddelbuettel, Dirk. 2013. Seamless R and C++ Integration with Rcpp. New York: Springer-Verlag.CrossRefzbMATHGoogle Scholar
  25. Ericksen, Wilhelm S. 1985. Inverse pairs of test matrices. ACM Transactions on Mathematical Software 11:302–304.MathSciNetCrossRefzbMATHGoogle Scholar
  26. Eubank, Randall L., and Ana Kupresanin. 2012. Statistical Computing in C++ and R. Boca Raton: Chapman and Hall/CRC Press.zbMATHGoogle Scholar
  27. 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.CrossRefzbMATHGoogle Scholar
  28. 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
  29. Gandrud, Christopher. 2015. Reproducible Research with R and R Studio, 2nd ed. Boca Raton: Chapman and Hall/CRC Press.zbMATHGoogle Scholar
  30. 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.zbMATHGoogle Scholar
  31. Gregory, Robert T., and David L. Karney. 1969. A Collection of Matrices for Testing Computational Algorithms. New York: John Wiley and Sons.zbMATHGoogle Scholar
  32. 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.zbMATHGoogle Scholar
  33. Gropp, William, Ewing Lusk, and Thomas Sterling (Editors). 2003. Beowulf Cluster Computing with Linux, 2nd ed. Cambridge, Massachusetts: The MIT Press.Google Scholar
  34. Hanson, Richard J., and Tim Hopkins. 2013. Numerical Computing with Modern Fortran. Philadelphia: Society for Industrial and Applied Mathematics.zbMATHGoogle Scholar
  35. Heroux, Michael A. 2015. Editorial: ACM TOMS replicated computational results initiative. ACM Transactions on Mathematical Software 41:Article No. 13.Google Scholar
  36. Higham, Nicholas J. 1991. Algorithm 694: A collection of test matrices in Matlab. ACM Transactions on Mathematical Software 17:289–305.CrossRefzbMATHGoogle Scholar
  37. Higham, Nicholas J. 2002. Accuracy and Stability of Numerical Algorithms, 2nd ed. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefzbMATHGoogle Scholar
  38. Karau, Holden, Andy Konwinski, Patrick Wendell, and Matei Zaharia. 2015. Learning Spark. Sabastopol, California: O’Reilly Media, Inc.Google Scholar
  39. 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.CrossRefzbMATHGoogle Scholar
  40. Lemmon, David R., and Joseph L. Schafer. 2005. Developing Statistical Software in Fortran 95. New York: Springer-Verlag.zbMATHGoogle Scholar
  41. Markus, Arjen. 2012. Modern Fortran in Practice. Cambridge, United Kingdom: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  42. Metcalf, Michael, John Reid, and Malcolm Cohen. 2011. Modern Fortran Explained. Oxford, United Kingdom: Oxford University Press.zbMATHGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. Quinn, Michael J. 2003. Parallel Programming in C with MPI and OpenMP. New York: McGraw-Hill.Google Scholar
  45. Rice, John R. 1993. Numerical Methods, Software, and Analysis, 2nd ed. New York: McGraw-Hill Book Company.zbMATHGoogle Scholar
  46. Roosta, Seyed H. 2000. Parallel Processing and Parallel Algorithms: Theory and Computation. New York: Springer-Verlag.CrossRefzbMATHGoogle Scholar
  47. 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
  48. 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.CrossRefzbMATHGoogle Scholar
  49. Stodden, Victoria, Friedrich Leisch, and Roger D. Peng. 2014. Implementing Reproducible Research. Boca Raton: Chapman and Hall/CRC Press.Google Scholar
  50. Venables, W. N., and B. D. Ripley. 2003. Modern Applied Statistics with S, 4th ed. New York: Springer-Verlag.zbMATHGoogle Scholar
  51. White, Tom. 2015. Hadoop: The Definitive Guide, 4th ed. Sabastopol, California: O’Reilly Media, Inc.Google Scholar
  52. Wickham, Hadley. 2015) Advanced R. Boca Raton: Chapman and Hall/CRC Press.Google Scholar
  53. Xie, Yihui. 2015. Dynamic Documents with R and knitr, 2nd ed. Boca Raton: Chapman and Hall/CRC Press.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • James E. Gentle
    • 1
  1. 1.FairfaxUSA

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