Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
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
LHKK01
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
DDHH2
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
DDDH3
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
DGL01
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).
DGL02
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
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Anda and H. Park. Fast plane rotations with dynamic scaling , SIAM J. matrix Anal. Appl., Vol. 15 (1994), pp. 162-174.
Baudin12
Baudin, R. Smith. A Robust Complex Division in Scilab , available from http://www.arxiv.org, arXiv:1210.4539v2 (2012).
Bischof00
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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
Demmel and K. Veselic. Jacobi’s method is more accurate than QR , SIAM J. Matrix Anal. Appl. 13(1992):1204-1246.
Demmel12
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
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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.
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Dhillon04
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
Dhillon, B. Parlett. Orthogonal Eigenvectors and * Relative Gaps , SIAM Journal on Matrix Analysis and Applications, Vol. 25, 2004. (Also LAPACK Working Note 154.)
Dhillon97
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
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
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
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
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
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
Golub and C. Van Loan. Matrix Computations , Johns Hopkins University Press, Baltimore, third edition,1996.
LUG
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
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
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 Solvers
Duff99
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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
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
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
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
Saad. Iterative Methods for Sparse Linear Systems. 2nd edition, SIAM, Philadelphia, PA, 2003.
Schenk00
Schenk. Scalable Parallel Sparse LU Factorization Methods on Shared Memory Multiprocessors . PhD thesis, ETH Zurich, 2000.
Schenk00-2
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
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
Schenk and K. Gartner. Two-level scheduling in PARDISO: Improved Scalability on Shared Memory Multiprocessing Systems . Parallel Computing, 28:187-197, 2002.
Schenk03
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
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
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
Polizzi, Density-Matrix-Based Algorithms for Solving Eigenvalue Problems , Phys. Rev. B. Vol. 79, 115112, 2009.
Polizzi12
Polizzi, A High-Performance Numerical Library for Solving Eigenvalue Problems: FEAST Solver v2.0 User’s Guide , arxiv.org/abs/1203.4031, 2012.
Bai00
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
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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.
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Vector Statistics (VS)
AVX
Intel. Intel® Advanced Vector Extensions Programming Reference, https://software.intel.com/content/www/us/en/develop/home.html .
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/content/www/us/en/develop/home.html<https://software.intel.com/content/www/us/en/develop/home.html>`_ .
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 .
LEcuyer94
L’Ecuyer, Pierre. Uniform Random Number Generation . Annals of Operations Research, 53, 77-120, 1994.
LEcuyer99
L’Ecuyer, Pierre. Tables of Linear Congruential Generators of Different Sizes and Good Lattice Structure . Mathematics of Computation, 68, 225, 249-260, 1999.
LEcuyer99a
L’Ecuyer, Pierre. Good Parameter Sets for Combined Multiple Recursive Random Number Generators . Operations Research, 47, 1, 159-164, 1999.
LEcuyer01
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
NAG Numerical Libraries. http://www.nag.co.uk/numeric/numerical_libraries.asp .
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. http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/earticles.html .
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).
SSNotes
Intel® oneMKL Summary Statistics Application Notes , a document present on the Intel® oneMKL product at https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-documentation.html .
VSNotes
Intel® oneMKL Vector Statistics Notes , a document present on the Intel® oneMKL product at https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-documentation.html .
VSData
Intel® oneMKL Vector Statistics Performance , a document present on the Intel® oneMKL product at https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-documentation.html .
Vector Mathematics (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.
VMData
Intel® oneMKL Vector Mathematics Performance and Accuracy , a document present on the Intel® oneMKL product at https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-documentation.html .
Fast Fourier Transforms (FFT)
FFT1
Oran Brigham, The Fast Fourier Transform and Its Applications , Prentice Hall, New Jersey, 1988.
FFT2
Athanasios Papoulis, The Fourier Integral and its Applications , 2nd edition, McGraw-Hill, New York, 1984.
FFT3
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.
FFT4
Charles Van Loan, Computational Frameworks for the Fast Fourier Transform , SIAM, Philadelphia, 1992.
Optimization Solvers
Conn00
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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 .