Guide and Reference

Appendix D. Bibliography

This bibliography lists the publications that you may need to use with ESSL and describes how to obtain them.

References

Text books and articles covering the mathematical aspects of ESSL are listed in this section, as well as several software libraries available from other companies. They are listed alphabetically as follows:

Each citation in the text of this book is shown as a number enclosed in square brackets. It indicates the number of the item listed in the bibliography. For example, reference [1] cites the first item listed below.

  1. Agarwal, R. C. Dec. 1984. "An Efficient Formulation of the Mixed-Radix FFT Algorithm." Proceedings of the International Conference on Computers, Systems, and Signal Processing, 769-772. Bangalore, India.

  2. Agarwal, R. C. August 1988. "A Vector and Parallel Implementation of the FFT Algorithm on the IBM 3090." Proceedings from the IFIP WG 2.5 (International Federation for Information Processing Working Conference 5), Stanford University.

  3. Agarwal, R. C. 1989. "A Vector and Parallel Implementation of the FFT Algorithm on the IBM 3090." Aspects of Computation on Asynchronous Parallel Processors, 45-54. Edited by M. H. Wright. Elsevier Science Publishers, New York, N. Y.

  4. Agarwal, R. C.; Cooley, J. W. March 1986. "Fourier Transform and Convolution Subroutines for the IBM 3090 Vector Facility." IBM Journal of Research and Development, 30(2):145-162 (Order no. G322-0146).

  5. Agarwal, R. C.; Cooley, J. W. September 1987. "Vectorized Mixed-Radix Discrete Fourier Transform Algorithms" IEEE Proceedings, 75:1283-1292.

  6. Agarwal, R.; Cooley, J.; Gustavson F.; Shearer J.; Slishman G.; Tuckerman B. March 1986. "New Scalar and Vector Elementary Functions for the IBM System/370." IBM Journal of Research and Development, 30(2):126-144 (Order no. G322-0146).

  7. Agarwal, R.; Gustavson F.; Zubair, M. May 1994. "An Efficient Parallel Algorithm for the 3-D FFT NAS Parallel Benchmark." Proceedings of IEEE SHPCC 94 :129-133.

  8. Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; DuCroz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. 1995. LAPACK User's Guide (second edition), SIAM Publications, Philadelphia, Pa. (For more information, see http://www.netlib.org/lapack/index.html.)

  9. Bathe, K.; Wilson, E. L. 1976. Numerical Methods in Finite Element Analysis, 249-258.

  10. Brayton, R. K.; Gustavson F. G.; Willoughby, R. A.; 1970. "Some Results on Sparse Matrices." Mathematics of Computation, 24(112):937-954.

  11. Borodin, A.; Munro, I. 1975. The Computational Complexity of Algebraic and Numeric Problems American Elsevier, New York, N. Y.

  12. Carey, G. F.; Oden, J. T. 1984. Finite Elements: Computational Aspects, Vol 3, 144-147. Prentice Hall, Englewood Cliffs, N. J.

  13. Chan, T. F. March 1982. "An Improved Algorithm for Computing the Singular Value Decomposition." ACM Transactions on Mathematical Software 8(1):72-83.

  14. Cline, A. K.; Moler, C. B.; Stewart, G. W.; Wilkinson, J. H. 1979. "An Estimate for the Condition Number of a Matrix." SIAM Journal of Numerical Analysis 16:368-375.

  15. Conte, S. D.; DeBoor, C. 1972. Elementary Numerical Analysis: An Algorithmic Approach (second edition), McGraw-Hill, New York, N. Y.

  16. Cooley, J. W. 1976. "Fast Fourier Transform." Encyclopedia of Computer Sciences Edited by A. Ralston. Auerbach Publishers.

  17. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. June 1967. "Application of the Fast Fourier Transform to Computation of Fourier Integrals, Fourier Series, and Convolution Integrals." IEEE Transactions Audio Electroacoustics AU-15:79-84.

  18. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. June 1967. "Historical Notes on the Fast Fourier Transform." IEEE Transactions Audio Electroacoustics AU-15:76-79. (Also published Oct. 1967 in Proceedings of IEEE 55(10):1675-1677.)

  19. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. March 1969. "The Fast Fourier Transform Algorithm and its Applications." IEEE Transactions on Education E12:27-34.

  20. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. June 1969. "The Finite Fast Fourier Transform." IEEE Transactions Audio Electroacoustics AU-17:77-85.

  21. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. July 1970. "The Fast Fourier Transform: Programming Considerations in the Calculation of Sine, Cosine, and LaPlace Transforms." Journal of Sound Vibration and Analysis 12(3):315-337.

  22. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. July 1970. "The Application of the Fast Fourier Transform Algorithm to the Estimation of Spectra and Cross-Spectra." Journal of Sound Vibration and Analysis 12(3):339-352.

  23. Cooley, J. W.; Lewis, P. A. W.; Welch, P. D. 1977. "Statistical Methods for Digital Computers." Mathematical Methods for Digital Computers Chapter 14. Edited by Ensein, Ralston and Wilf, Wiley-Interscience. John Wiley, New York.

  24. Cooley, J. W.; Tukey, J. W. April 1965. "An Algorithm for the Machine Calculation of Complex Fourier Series." Mathematics of Computation 19:297.

  25. Dahlquist, G.; Bjorck, A.; (Translated by Anderson, N.). 1974. Numerical Methods, Prentice Hall, Englewoods Cliffs, N. J. (For skyline subroutines, see 169-170.)

  26. Davis, P. J.; Rabinowitz, P. 1984. Methods of Numerical Integration, (second edition), Academic Press, Orlando, Florida.

  27. Delsarte, P.; Genin, Y. V. June 1986. "The Split Levinson Algorithm." IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP-34(3):472.

  28. Di Chio, P.; Filippone, S. January 1992. "A Stable Partition Sorting Algorithm." Report No. ICE-0045 IBM European Center for Scientific and Engineering Computing, Rome, Italy.

  29. Dodson, D. S.; Lewis, J. G. Jan. 1985. "Proposed Sparse Extensions to the Basic Linear Algebra Subprograms." ACM SIGNUM Newsletter, 20(1).

  30. Dongarra, J. J. July 1997. "Performance of Various Computers Using Standard Linear Equations Software." University of Tennessee, CS-89-85. (You can download this document from http://www.netlib.org/benchmark/performance.ps.)

  31. Dongarra, J. J.; Bunch, J. R.; Moler C. B.; Stewart, G. W. 1986. LINPACK User's Guide, SIAM Publications, Philadelphia, Pa. (For more information, see http://www.netlib.org/linpack/index.html.)

  32. Dongarra, J. J.; DuCroz, J.; Hammarling, S.; Duff, I. March 1990. "A Set of Level 3 Basic Linear Algebra Subprograms." ACM Transactions on Mathematical Software, 16(1):1-17.

  33. Dongarra, J. J.; DuCroz, J.; Hammarling, S.; Duff, I. March 1990. "Algorithm 679. A Set of Level 3 Basic Linear Algebra Subprograms: Model Implementation and Test Programs." ACM Tranactions on Mathematical Software, 16(1):18-28.

  34. Dongarra, J. J.; DuCroz, J.; Hammarling, S.; Hanson, R. J. March 1988. "An Extended Set of Fortran Basic Linear Algebra Subprograms." ACM Transactions on Mathematical Software, 14(1):1-17.

  35. Dongarra, J. J.; DuCroz, J.; Hammarling, S.; Hanson, R. J. March 1988. "Algorithm 656. An Extended Set of Basic Linear Algebra Subprograms: Model Implementation and Test Programs." ACM Tranactions on Mathematical Software, 14(1):18-32.

  36. Dongarra, J. J.; Duff, I. S.; Sorensen, D. C.; Van der Vorst, H. 1991. Solving Linear Systems on Vector and Shared Memory Computers, SIAM Publications, ISBN 0-89871-270-X.

  37. Dongarra, J. J.; Eisenstat, S. C. May 1983. "Squeezing the Most Out of an Algorithm in Cray Fortran." Technical Memorandum 9 Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439.

  38. Dongarra, J. J.; Gustavson, F. G.; Karp, A. Jan. 1984. "Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine." SIAM Review, 26(1).

  39. Dongarra, J. J.; Kaufman, L.; Hammarling, S. Jan. 1985. "Squeezing the Most Out of Eigenvalue Solvers on High-Performance Computers." Technical Memorandum 46 Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439.

  40. Dongarra, J. J.; Kolatis M. October 1994. "Call Conversion Interface (CCI) for LAPACK/ESSL." LAPACK Working Note 82, Department of Computer Science University of Tennessee, Knoxville, Tennessee. (You can download this document from http://www.netlib.org/lapack/lawns/lawn82.ps.)

  41. Dongarra, J. J.; Kolatis M. May 1994. "IBM RS/6000-550 & -590 Performance for Selected Routines in ESSL/LAPACK/NAG/IMSL", LAPACK Working Note 71, Department of Computer Science University of Tennessee, Knoxville, Tennessee. (You can download this document from http://www.netlib.org/lapack/lawns/lawn71.ps.)

  42. Dongarra, J. J; Meuer, H. W.; Strohmaier, E. June 1997. "Top500 Supercomputer Sites." University of Tennessee, UT-CS-97-365.; University of Mannheim, RUM 50/97, (You can view this document from http://www.netlib.org/benchmark/top500.html.)

  43. Dongarra, J. J.; Moler, C. B. August 1983. "EISPACK--A Package for Solving Matrix Eigenvalue Problems." Technical Memorandum 12 Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439.

  44. Dongarra, J. J.; Moler, C. B; Bunch, J. R.; Stewart, G. W. 1979. LINPACK Users' Guide, SIAM, Philadelphia, Pa.

  45. Dubrulle, A. A. 1971. "QR Algorithm with Implicit Shift." IBM licensed program: PL/MATH.

  46. Dubrulle, A. A. November 1979. "The Design of Matrix Algorithms for Fortran and Virtual Storage." IBM Palo Alto Scientific Center Technical Report (Order no. G320-3396).

  47. Duff, I. S.; Erisman, A. M.; Reid, J. K. 1986. Direct Methods for Sparse Matrices Oxford University Press (Claredon), Oxford. (For skyline subroutines, see 151-153.)

  48. Eisenstat, S. C. March 1981. "Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods." SIAM Journal of Scientific Statistical Computing, 2(1).

  49. EISPACK software library; National Energy Software Center, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 (312-972-7250); International Mathematical and Statistical Libraries, Inc., Sixth Floor, GNB Building, 7500 Bellaire Boulevard, Houston, Texas 77036 (713-772-1927)

  50. Filippone, S.; Santangelo, P.; Vitaletti M. Nov. 1990. "A Vectorized Long-Period Shift Register Random Number Generation." Proceedings of Supercomputing '90, 676-684, New York.

  51. Forsythe, G. E.; Malcolm, M. A. 1977. Computer Methods for Mathematical Computations, Prentice Hall, Englewoods Cliffs, N. J.

  52. Forsythe, G.E.; Moler, C. 1967. Computer Solution of Linear Algebra Systems, Prentice Hall, Englewoods Cliffs, N. J.

  53. Freund, R. W. July 28, 1992. "Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems." Numerical Analysis Manuscript 92-07 AT&T Bell Laboratories. (To appear in SIAM Journal of Scientific Statistical Computing, 1993, Vol. 14.)

  54. Gans, D. 1969. Transformations and Geometries Appleton Century Crofts, New York.

  55. Garbow, B. S.; Boyle, J. M.; Dongarra, J. J.; Moler, C. B. 1977. "Matrix Eigensystem Routines." EISPACK Guide Extension Lecture Notes in Computer Science, Vol. 51 Springer-Verlag, New York, Heidelberg, Berlin.

  56. George, A.; Liu, J. W. 1981. "Computer Solution of Large Sparse Positive Definite Systems." Series in Computational Mathematics Prentice-Hall, Englewood Cliffs, New Jersey.

  57. Gerald, C. F.; Wheatley, P. O. 1985. Applied Numerical Analysis (third edition), Addison-Wesley, Reading, Mass.

  58. Gill, P. E.; Miller, G. R. 1972. "An Algorithm for the Integration of Unequally Spaced Data." Computer Journal 15:80-83.

  59. Golub, G. H.; Van Loan, C. F. 1996. Matrix Computations, John Hopkins University Press, Baltimore, Maryland.

  60. Gregory, R. T.; Karney, D. L. 1969. A Collection of Matrices for Testing Computational Algorithms, Wiley-Interscience, New York, London, Sydney, Toronto.

  61. Grimes, R. C.; Kincaid, D. R.; Young, D. M. 1979. ITPACK 2.0 User's Guide, CNA-150. Center for Numerical Analysis, University of Texas at Austin.

  62. Hageman, L. A.; Young, D. M.. 1981. Applied Iterative Methods Academic Press, New York, N. Y.

  63. Higham, N. J. 1996. Accuracy and Stability of Numerical Algorithms, SIAM Publications, Philadelphia, Pa.

  64. Higham, N. J. December 1988. Fortran Codes for Estimating the One-Norm of a Real or Complex Matrix, with Application to Condition Estimating ACM Transactions on Mathematical Software, 14(4):381-396.

  65. Jennings, A. 1977. Matrix Computation for Engineers and Scientists, 153-158, John Wiley and Sons, Ltd., New York, N. Y.

  66. Kagstrom, B.; Ling, P.; Van Loan, C. 1993. "Portable High Performance GEMM-Based Level 3 BLAS", Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, 339-346. Edited by: R. Sincovec, D. Keyes, M. Leize, L. Petzold, and D. Reed. SIAM Publications.

  67. Kincaid, D. R.; Oppe, T. C.; Respess, J. R.; Young, D. M. 1984. ITPACKV 2C User's Guide, CNA-191. Center for Numerical Analysis, University of Texas at Austin.

  68. Kirkpatrick, S.; Stoll, E. P. 1981. "A Very Fast Shift-Register Sequence Random Number Generation." Journal of Computational Physics, 40:517-526.

  69. Knuth, D. E. 1973. The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley, Reading, Mass.

  70. Knuth, D. E. 1981. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, (second edition), Addison-Wesley, Reading, Mass.

  71. Lambiotte, J. J.; Voigt, R. G. December 1975. "The Solution of Tridiagonal Linear Systems on the CDC STAR-100 Computer." ACM Transactions on Mathematical Software 1(4):308-329.

  72. Lawson, C. L.; Hanson, R. J. 1974. Solving Least Squares Problems Prentice-Hall, Englewood Cliffs, New Jersey.

  73. Lawson, C. L.; Hanson, R. J.; Kincaid, D. R.; Krough, F. T. Sept. 1979. "Basic Linear Algebra Subprograms for Fortran Usage." ACM Transactions on Mathematical Software 5(3):308-323.

  74. Lewis, P. A. W.; Goodman, A. S.; Miller, J. M. 1969. "A Pseudo-Random Number Generator for the System/360." IBM System Journal, 8(2).

  75. McCracken, D. D.; Dorn, W. S. 1964. Numerical Methods and Fortran Programming, John Wiley and Sons, New York.

  76. Melhem, R. 1987. "Toward Efficient Implementation of Preconditioned Conjugate Gradient Methods on Vector Supercomputers." Journal of Supercomputer Applications, Vol. 1.

  77. Moler, C. B.; Stewart, G. W. 1973. "An Algorithm for the Generalized Matrix Eigenvalue Problem." SIAM Journal of Numerical Analysis, 10:241-256.

  78. Oppenheim, A. V.; Schafer, R. W. 1975. Digital Signal Processing Prentice-Hall, Englewood Cliffs, New Jersey.

  79. Oppenheim, A. V.; Weinstein, C. August 1972. "Effects of Finite Register Length in Digital Filtering and the Fast Fourier Transform." IEEE Proceedings, AU-17:209-215.

  80. Saad, Y.; Schultz, M. H. 1986. "GMRES: A Generalized Minimum Residual Algorithm for Solving Nonsymmetric Linear Systems." SIAM Journal of Scientific and Statistical Computing, 7:856-869. Philadelphia, Pa.

  81. Smith, B. T.; Boyle, J. M.; Dongarra, J. J.; Garbow, B. S.; Ikebe, Y.; Klema, V. C.; Moler, C. B. 1976. "Matrix Eigensystem Routines." EISPACK Guide Lecture Notes in Computer Science, Vol. 6 Springer-Verlag, New York, Heidelberg, Berlin.

  82. Sonneveld; Wesseling; DeZeeuv. 1985. Multigrid and Conjugate Gradient Methods as Convergence Acceleration Techniques in Multigrid Methods for Integral and Differential Equations, 117-167. Edited by D.J. Paddon and M. Holstein. Oxford University Press (Claredon), Oxford.

  83. Sonneveld, P. January 1989. "CGS, a Fast Lanczos-Type Solver for Nonsymmetric Linear Systems." SIAM Journal of Scientific and Statistical Computing, 10(1):36-52.

  84. Stewart, G. 1973. Introduction to Matrix Computations Academic Press, New York, N. Y.

  85. Stewart, G. W. 1976. "The Economical Storage of Plane Rotations." Numerische Mathematik, 25(2):137-139.

  86. Stroud, A. H.; Secrest, D. 1966. Gaussian Quadrature Formulas Prentice-Hall, Englewood Cliffs, New Jersey.

  87. Suhl, U. H.; Aittoniemi, L. 1987. "Computing Sparse LU-Factorization for Large-Scale Linear Programming Bases." Report Number 58 Freie University, Berlin.

  88. Tausworthe, R. C. 1965. "Random Numbers Generated by Linear Recurrence Modulo Two." Mathematical Computing, Vol. 19

  89. Van der Vorst, H. A. 1992. "Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems." SIAM Journal of Scientific Statistical Computing, 13:631-644.

  90. Weinstein, C. September 1969. "Round-off Noise in Floating Point Fast Fourier Transform Calculation." IEEE Transactions on Audio Electroacoustics AU-17:209-215.

  91. Wilkinson, J. H. 1965. The Algebraic Eigenvalue Problem, Oxford University Press (Claredon), Oxford.

  92. Wilkinson, J. H. 1963. Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, New Jersey.

  93. Wilkinson, J. H.; Reinsch, C. 1971. Handbook for Automatic Computation, Vol. II, Linear Algebra, Springer-Verlag, New York, Heidelberg, Berlin.

  94. Zierler, N. 1969 "Primitive Trinomials Whose Degree Is a Mersenne Exponent." Information and Control, 15:67-69.

  95. Zlatev, Z. 1980. "On Some Pivotal Strategies in Gaussian Elimination by Sparse Technique." SIAM Journal of Numerical Analysis, 17(1):18-30.

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