A Look at the Evolution of Mathematical Software for Dense Matrix Problems over the Past Fifteen Years

  • J. J. Dongarra
  • D. C. Sorensen
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 13)


In this paper we look at the evolution which has taken place in the design of mathematical software for dense matrix problems. Our main emphasis is on algorithms for solving linear algebra problems where the software we develop would reside in a library on high-performance computers.


Linear Algebra Memory Reference Argonne National Laboratory Mathematical Software Vector Operation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Dongarra, J. Bunch, C. Moler, and G. Stewart, UNPACK Users’ Guide, SIAM Pub, Philadelpha (1976).Google Scholar
  2. 2.
    J. Dongarra and Stanley C. Eisenstat, “Squeezing the Most out of an Algorithm in Cray Fortran,” ACM Trans. Math. Software 10, 3, pp. 221–230 (1984).CrossRefGoogle Scholar
  3. 3.
    J.J. Dongarra, “Performance of Various Computers Using Standard Linear Equations Software in a Fortran Environment,” Argonne National Laboratory MCS-TM-23 (October 1986).Google Scholar
  4. 4.
    J.J. Dongarra, L. Kaufman, and S. Hammarling, “Squeezing the Most Out of High Performance Computers for Finding the Eigenvalues,” Linear Algebra and Its Applications 77, pp. 113–136 (1986).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    J.J. Dongarra and D.C. Sorensen, “Linear Algebra on High-Performance Computers,” pp. 3–32 in Proceedings Parallel Computing 85, ed. U. Schendel, North Holland (1986).Google Scholar
  6. 6.
    B.S. Garbow, J.M. Boyle, J.J. Dongarra, and C.B. Moler, Matrix Eigensystem Routines — EISPACK Guide Extension, 1977.MATHGoogle Scholar
  7. 7.
    C. Lawson, R. Hanson, D. Kincaid, and and F. Krogh, “Basic Linear Algebra Subprograms for Fortran Usage,” ACM Transactions on Mathematical Software, pp. 308–323 (1979).Google Scholar
  8. 8.
    B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe, V. Klema, and C. Moler, Matrix Eigensystem RoutinesEISPACK Guide, Second Edition., 1976.Google Scholar
  9. 9.
    J. Wilkinson and C. Reinsch, Handbook for Automatic Computation: Volume IILinear Algebra, Springer-Verlag, New YorkGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • J. J. Dongarra
    • 1
  • D. C. Sorensen
    • 2
  1. 1.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA
  2. 2.Center for Supercomputing Research and Development, 305 Talbot LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations