Developer Reference

  • 2021.1
  • 12/04/2020
  • 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.
    A Scalable Sparse Direct Solver Using Static Pivoting
    . In Proceeding of the 9th SIAM conference on Parallel Processing for Scientific Computing, San Antonio, Texas, March 22-34,1999.
    [Liu85]
    J.W.H. Liu.
    Modification of the Minimum-Degree algorithm by multiple elimination
    . ACM Transactions on Mathematical Software, 11(2):141-153, 1985.
    [Menon98]
    R. Menon L. Dagnum.
    OpenMP: An Industry-Standard API for Shared-Memory Programming
    . IEEE Computational Science & Engineering, 1:46-55, 1998. http://www.openmp.org.
    [Saad03]
    Y. Saad.
    Iterative Methods for Sparse Linear Systems.
    2nd edition, SIAM, Philadelphia, PA, 2003.
    [Schenk00]
    O. Schenk.
    Scalable Parallel Sparse LU Factorization Methods on Shared Memory Multiprocessors
    . PhD thesis, ETH Zurich, 2000.
    [Schenk00-2]
    O. Schenk, K. Gartner, and W. Fichtner.
    Efficient Sparse LU Factorization with Left-right Looking Strategy on Shared Memory Multiprocessors
    . BIT, 40(1):158-176, 2000.
    [Schenk01]
    O. Schenk and K. Gartner.
    Sparse Factorization with Two-Level Scheduling in PARDISO
    . In Proceeding of the 10th SIAM conference on Parallel Processing for Scientific Computing, Portsmouth, Virginia, March 12-14, 2001.
    [Schenk02]
    O. Schenk and K. Gartner.
    Two-level scheduling in PARDISO: Improved Scalability on Shared Memory Multiprocessing Systems
    . Parallel Computing, 28:187-197, 2002.
    [Schenk03]
    O. Schenk and K. Gartner.
    Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
    . Journal of Future Generation Computer Systems, 20(3):475-487, 2004.
    [Schenk04]
    O. Schenk and K. Gartner.
    On Fast Factorization Pivoting Methods for Sparse Symmetric Indefinite Systems
    . Technical Report, Department of Computer Science, University of Basel, 2004, submitted.
    [Sonn89]
    P. Sonneveld.
    CGS, a Fast Lanczos-Type Solver for Nonsymmetric Linear Systems
    . SIAM Journal on Scientific and Statistical Computing, 10:36-52, 1989.
    [Young71]
    D.M.Young.
    Iterative Solution of Large Linear Systems
    . New York, Academic Press, Inc., 1971.
  • Extended Eigensolver
    [Polizzi09]
    E. Polizzi,
    Density-Matrix-Based Algorithms for Solving Eigenvalue Problems
    , Phys. Rev. B. Vol. 79, 115112, 2009.
    [Polizzi12]
    E. Polizzi,
    A High-Performance Numerical Library for Solving Eigenvalue Problems: FEAST Solver v2.0 User's Guide
    , arxiv.org/abs/1203.4031, 2012.
    [Bai00]
    Z. Bai, J. Demmel, J. Dongarra, A. Ruhe and H. van der Vorst, editors,
    Templates for the solution of Algebraic Eigenvalue Problems: A Practical Guide
    . SIAM, Philadelphia, 2000.
    [Sleijpen96]
    G. L. G. Sleijpen and H. A. van der Vorst.
    A Jacobi-Davidson iteration method for linear eigenvalue problems
    . SIAM J. Matrix Anal. Appl., 17:401-425, 1996.
  • VS
    [AVX]
    Intel.
    Intel® Advanced Vector Extensions Programming Reference
    . (https://software.intel.com/file/36945)
    [Billor00]
    Nedret Billor, Ali S. Hadib, and Paul F. Velleman.
    BACON: blocked adaptive computationally efficient outlier nominators
    . Computational Statistics & Data Analysis, 34, 279-298, 2000.
    [Bratley87]
    Bratley P., Fox B.L., and Schrage L.E.
    A Guide to Simulation
    . 2nd edition. Springer-Verlag, New York, 1987.
    [Bratley88]
    Bratley P. and Fox B.L.
    Implementing Sobol's Quasirandom Sequence Generator
    , ACM Transactions on Mathematical Software, Vol. 14, No. 1, Pages 88-100, March 1988.
    [Bratley92]
    Bratley P., Fox B.L., and Niederreiter H.
    Implementation and Tests of Low-Discrepancy Sequences
    , ACM Transactions on Modeling and Computer Simulation, Vol. 2, No. 3, Pages 195-213, July 1992.
    [BMT]
    Intel.
    Bull Mountain Technology Software Implementation Guide
    . (https://software.intel.com/file/37157)
    [Coddington94]
    Coddington, P. D.
    Analysis of Random Number Generators Using Monte Carlo Simulation
    . Int. J. Mod. Phys. C-5, 547, 1994.
    [Fritsch80]
    Fritsch, F. N and Carlson, R. E.
    Monotone Piecewise Cubic Interpolation
    . SIAM Journal on Numerical Analysis (SIAM) 17 (2): 238-246, 1980.
    [Gentle98]
    Gentle, James E.
    Random Number Generation and Monte Carlo Methods
    , Springer-Verlag New York, Inc., 1998.
    [Hyman83]
    Hyman, J. M.
    Accurate monotonicity preserving cubic interpolation
    , SIAM J. Sci. Stat. Comput. 4, 645-654, 1983.
    [IntelSWMan]
    Intel.
    Intel® 64 and IA-32 Architectures Software Developer’s Manual
    . 3 vols. (https://software.intel.com/content/www/us/en/develop/articles/intel-sdm.html)
    [L'Ecuyer94]
    L'Ecuyer, Pierre.
    Uniform Random Number Generation
    . Annals of Operations Research, 53, 77-120, 1994.
    [L'Ecuyer99]
    L'Ecuyer, Pierre.
    Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure
    . Mathematics of Computation, 68, 225, 249-260, 1999.
    [L'Ecuyer99a]
    L'Ecuyer, Pierre.
    Good Parameter Sets for Combined Multiple Recursive Random Number Generators
    . Operations Research, 47, 1, 159-164, 1999.
    [L'Ecuyer01]
    L'Ecuyer, Pierre.
    Software for Uniform Random Number Generation: Distinguishing the Good and the Bad
    . Proceedings of the 2001 Winter Simulation Conference, IEEE Press, 95-105, Dec. 2001.
    [Kirkpatrick81]
    Kirkpatrick, S., and Stoll, E.
    A Very Fast Shift-Register Sequence Random Number Generator
    . Journal of Computational Physics, V. 40. 517-526, 1981.
    [Knuth81]
    Knuth, Donald E.
    The Art of Computer Programming, Volume 2, Seminumerical Algorithms
    . 2nd edition, Addison-Wesley Publishing Company, Reading, Massachusetts, 1981.
    [Maronna02]
    Maronna, R.A., and Zamar, R.H.,
    Robust Multivariate Estimates for High-Dimensional Datasets
    , Technometrics, 44, 307-317, 2002.
    [Matsumoto98]
    Matsumoto, M., and Nishimura, T.
    Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator
    , ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, Pages 3-30, January 1998.
    [Matsumoto00]
    Matsumoto, M., and Nishimura, T.
    Dynamic Creation of Pseudorandom Number Generators
    , 56-69, in: Monte Carlo and Quasi-Monte Carlo Methods 1998, Ed. Niederreiter, H. and Spanier, J., Springer 2000, http://www.math.sci.hiroshima-u.ac.jp/%7Em-mat/MT/DC/dc.html.
    [NAG]
    [Rocke96]
    David M. Rocke,
    Robustness properties of S-estimators of multivariate location and shape in high dimension
    . The Annals of Statistics, 24(3), 1327-1345, 1996.
    [Saito08]
    Saito, M., and Matsumoto, M.
    SIMD-oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator
    . Monte Carlo and Quasi-Monte Carlo Methods 2006, Springer, Pages 607 – 622, 2008.
    [Salmon11]
    Salmon, John K., Morales, Mark A., Dror, Ron O., and Shaw, David E.,
    Parallel Random Numbers: As Easy as 1, 2, 3
    . SC '11 Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, 2011.
    [Schafer97]
    Schafer, J.L.,
    Analysis of Incomplete Multivariate Data
    . Chapman & Hall, 1997.
    [Sobol76]
    Sobol, I.M., and Levitan, Yu.L.
    The production of points uniformly distributed in a multidimensional cube
    . Preprint 40, Institute of Applied Mathematics, USSR Academy of Sciences, 1976 (In Russian).
    [SSL Notes]
    Intel® oneMKL
    Summary Statistics Application Notes
    , a document present on the
    Intel® oneMKL
    product at https://software.intel.com/content/www/us/en/develop/articles/intel-math-kernel-library-documentation.html
    [VS Notes]
    Intel® oneMKL
    Vector Statistics Notes
    , a document present on the
    Intel® oneMKL
    product at https://software.intel.com/content/www/us/en/develop/articles/intel-math-kernel-library-documentation.html
    [VS Data]
    Intel® oneMKL
    Vector Statistics Performance
    , a document present on the
    Intel® oneMKL
    product at https://software.intel.com/content/www/us/en/develop/articles/intel-math-kernel-library-documentation.html
  • VM
    [C99]
    ISO/IEC 9899:1999/Cor 3:2007. Programming languages -- C.
    [Muller97]
    J.M.Muller.
    Elementary functions: algorithms and implementation
    , Birkhauser Boston, 1997.
    [IEEE754]
    IEEE Standard for Binary Floating-Point Arithmetic. ANSI/IEEE Std 754-2008.
    [VM Data]
    Intel® oneMKL
    Vector Mathematics Performance and Accuracy
    , a document present on the
    Intel® oneMKL
    product at https://software.intel.com/content/www/us/en/develop/articles/intel-math-kernel-library-documentation.html
  • FFT
    [1]
    E. Oran Brigham,
    The Fast Fourier Transform and Its Applications
    , Prentice Hall, New Jersey, 1988.
    [2]
    Athanasios Papoulis,
    The Fourier Integral and its Applications
    , 2nd edition, McGraw-Hill, New York, 1984.
    [3]
    Ping Tak Peter Tang,
    DFTI - a new interface for Fast Fourier Transform libraries
    , ACM Transactions on Mathematical Software, Vol. 31, Issue 4, Pages 475 - 507, 2005.
    [4]
    Charles Van Loan,
    Computational Frameworks for the Fast Fourier Transform
    , SIAM, Philadelphia, 1992.
  • Optimization Solvers
    [Conn00]
    A. R. Conn, N. I.M. Gould, P. L. Toint.
    Trust-region Methods.
    SIAM Society for Industrial & Applied Mathematics, Englewood Cliffs, New Jersey, MPS-SIAM Series on Optimization edition, 2000.
  • Data Fitting Functions
    [deBoor2001]
    Carl deBoor.
    A Practical Guide to Splines.
    Revised Edition. Springer-Verlag New York Berlin Heidelberg, 2001.
    [Schumaker2007]
    Larry L Schumaker.
    Spline Functions: Basic Theory.
    3
    rd
    Edition. Cambridge University Press, Cambridge, 2007.
    [StechSub76]
    S.B. Stechhkin, and Yu Subbotin.
    Splines in Numerical Mathematics.
    Izd. Nauka, Moscow, 1976.
For a reference implementation of BLAS, sparse BLAS, LAPACK, and ScaLAPACK packages visit www.netlib.org.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.