Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

Bibliography

For more information about the
BLAS, Sparse BLAS, LAPACK, ScaLAPACK, Sparse Solver, Extended Eigensolver, VM,
VS
, FFT, and Non-Linear Optimization Solvers
functionality, refer to the following publications:
  • BLAS Level 1
    C. Lawson, R. Hanson, D. Kincaid, and F. Krough.
    Basic Linear Algebra Subprograms for Fortran Usage
    , ACM Transactions on Mathematical Software, Vol.5, No.3 (September 1979) 308-325.
  • BLAS Level 2
    J. Dongarra, J. Du Croz, S. Hammarling, and R. Hanson.
    An Extended Set of Fortran Basic Linear Algebra Subprograms
    , ACM Transactions on Mathematical Software, Vol.14, No.1 (March 1988) 1-32.
  • BLAS Level 3
    J. Dongarra, J. DuCroz, I. Duff, and S. Hammarling.
    A Set of Level 3 Basic Linear Algebra Subprograms
    , ACM Transactions on Mathematical Software (December 1989).
  • Sparse BLAS
    D. Dodson, R. Grimes, and J. Lewis.
    Sparse Extensions to the FORTRAN Basic Linear Algebra Subprograms
    , ACM Transactions on Math Software, Vol.17, No.2 (June 1991).
    D. Dodson, R. Grimes, and J. Lewis.
    Algorithm 692: Model Implementation and Test Package for the Sparse Basic Linear Algebra Subprograms
    , ACM Transactions on Mathematical Software, Vol.17, No.2 (June 1991).
    [Duff86]
    I.S.Duff, A.M.Erisman, and J.K.Reid.
    Direct Methods for Sparse Matrices
    . Clarendon Press, Oxford, UK, 1986.
    [CXML01]
    Compaq Extended Math Library
    . Reference Guide, Oct.2001.
    [Rem05]
    K.Remington.
    A NIST FORTRAN Sparse Blas User's Guide
    . (available on http://math.nist.gov/~KRemington/fspblas/ )
    [Saad94]
    Y.Saad. SPARSKIT:
    A Basic Tool-kit for Sparse Matrix Computation
    . Version 2, 1994.( http://www.cs.umn.edu/~saad )
    [Saad96]
    Y.Saad.
    Iterative Methods for Linear Systems
    . PWS Publishing, Boston, 1996.
  • LAPACK
    [AndaPark94]
    A. A. Anda and H. Park.
    Fast plane rotations with dynamic scaling
    , SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174.
    [Baudin12]
    M. Baudin, R. Smith.
    A Robust Complex Division in Scilab
    , available from http://www.arxiv.org, arXiv:1210.4539v2 (2012).
    [Bischof00]
    C. H. Bischof, B. Lang, and X. Sun.
    Algorithm 807: The SBR toolbox-software for successive band reduction
    , ACM Transactions on Mathematical Software, Vol. 26, No. 4, pages 602-616, December 2000.
    [Demmel92]
    J. Demmel and K. Veselic.
    Jacobi's method is more accurate than QR
    , SIAM J. Matrix Anal. Appl. 13(1992):1204-1246.
    [Demmel12]
    J. Demmel, L. Grigori, M. F. Hoemmen, and J. Langou.
    Communication-optimal parallel and sequential QR and LU factorizations
    , SIAM Journal on Scientific Computing, Vol. 34, No 1, 2012.
    [deRijk98]
    P. P. M. De Rijk.
    A one-sided Jacobi algorithm for computing the singular value decomposition on a vector computer
    , SIAM J. Sci. Stat. Comp., Vol. 10 (1998), pp. 359-371.
    [Dhillon04]
    I. Dhillon, B. Parlett.
    Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
    , Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
    [Dhillon04-02]
    I. Dhillon, B. Parlett.
    Orthogonal Eigenvectors and * Relative Gaps
    , SIAM Journal on Matrix Analysis and Applications, Vol. 25, 2004. (Also LAPACK Working Note 154.)
    [Dhillon97]
    I. Dhillon.
    A new O(n^2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem
    , Computer Science Division Technical Report No. UCB/CSD-97-971, UC Berkeley, May 1997.
    [Drmac08-1]
    Z. Drmac and K. Veselic.
    New fast and accurate Jacobi SVD algorithm I
    , SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1322-1342. LAPACK Working note 169.
    [Drmac08-2]
    Z. Drmac and K. Veselic.
    New fast and accurate Jacobi SVD algorithm II
    , SIAM J. Matrix Anal. Appl. Vol. 35, No. 2 (2008), pp. 1343-1362. LAPACK Working note 170.
    [Drmac08-3]
    Z. Drmac and K. Bujanovic.
    On the failure of rank-revealing QR factorization software - a case study
    , ACM Trans. Math. Softw. Vol. 35, No 2 (2008), pp. 1-28. LAPACK Working note 176.
    [Drmac08-4]
    Z. Drmac.
    Implementation of Jacobi rotations for accurate singular value computation in floating point arithmetic
    , SIAM J. Sci. Comp., Vol. 18 (1997), pp. 1200-1222.
    [Elmroth00]
    E. Elmroth and F. Gustavson.
    Applying Recursion to Serial and Parallel QR Factorization Leads to Better Performance
    , IBM J. Research & Development, Vol. 44, No. 4, 2000, pp 605-624.
    [Golub96]
    G. Golub and C. Van Loan.
    Matrix Computations
    , Johns Hopkins University Press, Baltimore, third edition,1996.
    [LUG]
    E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen.
    LAPACK Users' Guide
    , Third Edition, Society for Industrial and Applied Mathematics (SIAM), 1999.
    [Kahan66]
    W. Kahan.
    Accurate Eigenvalues of a Symmetric Tridiagonal Matrix
    , Report CS41, Computer Science Dept., Stanford University, July 21, 1966.
    [Marques06]
    O.Marques, E.J.Riedy, and Ch.Voemel.
    Benefits of IEEE-754 Features in Modern Symmetric Tridiagonal Eigensolvers
    , SIAM Journal on Scientific Computing, Vol.28, No.5, 2006. (Tech report version in LAPACK Working Note 172 with the same title.)
    [Sutton09]
    Brian D. Sutton.
    Computing the complete CS decomposition
    , Numer. Algorithms, 50(1):33-65, 2009.
  • ScaLAPACK
    [SLUG]
    L. Blackford, J. Choi, A.Cleary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K.Stanley, D. Walker, and R. Whaley.
    ScaLAPACK Users' Guide
    , Society for Industrial and Applied Mathematics (SIAM), 1997.
  • Sparse Solver
    [Duff99]
    I. S. Duff and J. Koster.
    The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices.
    SIAM J. Matrix Analysis and Applications, 20(4):889-901, 1999.
    [Dong95]
    J. Dongarra, V.Eijkhout, A.Kalhan.
    Reverse Communication Interface for Linear Algebra Templates for Iterative Methods
    . UT-CS-95-291, May 1995. http://www.netlib.org/lapack/lawnspdf/lawn99.pdf
    [Karypis98]
    G. Karypis and V. Kumar.
    A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
    . SIAM Journal on Scientific Computing, 20(1):359-392, 1998.
    [Li99]
    X.S. Li and J.W. Demmel.