More accuracy at fixed precision

Journal of Computational and Applied Mathematics

Volumn 162, Issue 1, 2004, Pages 57-77

  Langlois, Philippe ^a  

^a UNIVERSITÉ DE PERPIGNAN   (France)

Author keywords

Accuracy; Automatic correction; CENA method; Finite precision; Floating point arithmetic

Indexed keywords

ALGORITHMS; COMPUTER SOFTWARE; ERROR CORRECTION;

FIXED FINITE PRECISION; RESIDUAL ERROR;

COMPUTATIONAL METHODS;

MATHEMATICAL ANALYSIS; PRECISION;

EID: 0348015851     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.08.017     Document Type: Article

References (37)

1. D.H. Bailey, A Fortran-90 double-double library, 2001. Available at URL:http://www.nersc.gov/~dhb/mpdist/mpdist.html
2. Blackford L.S. Demmel J. Dongarra J. Duff I. Hammarling S. Henry G. Heroux M. Kaufman L. Lumsdaine A. Petitet A. Pozo R. Remington K. Whaley R.C. An updated set of basic linear algebra subprograms (BLAS) ACM Trans. Math. Software 28 2 2002 135-151
3. Bohlender G. Floating-point computation of functions with maximum accuracy IEEE Trans. Comput. C-26 7 1977 621-632
4. K. Briggs, Doubledouble floating point arithmetic, 1998. Available at URL:http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html
5. J.-M. Chesneaux, Stochastic arithmetic and CADNA software, Habilitation à diriger des recherches, Université P. et M. Curie, Paris, France, November 1995 (in French).
6. J.-M. Chesneaux, S. Guilain, J. Vignes, La bibliothèque CADNA: Présentation et utilisation, Manual, Laboratoire d'Informatique de Paris 6, Université P. et M. Curie, Paris, France, November 1996. Available at URL: http://www-anp.lip6.fr/cadna/
7. G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann (Eds.), Automatic Differentiation Algorithms: From Simulation to Optimization, Computer and Information Science, Springer, New York, 2001.
8. Dahlquist G. Björck Å. Numerical Methods 1974 Prentice-Hall Englewood Cliffs, NJ, USA
9. Daumas M. Langlois P. Additive symmetries: The non-negative case Theoret. Comput. Sci. 291 2 2003 143-157
10. Dekker T.J. A floating-point technique for extending the available precision Numer. Math. 18 1971 224-242
11. J.W. Demmel, Recent progress in high accuracy and high performance linear algebra algorithms, SIAM Annual Meeting, May 1999. Available at URL:http://www.cs.berkeley.edu/~demmel
12. J.W. Demmel, Y. Hida, Accurate floating point summation, Report UCB/CSD-02-1180, Department of Computer Science, University of California, May 2002.
13. Document for the Basic Linear Algebra Subprograms (BLAS) standard, February 2001. URL:http://www.netlib.org/utk/papers/blast-forum.html
14. Griewank A. Evaluating Derivatives. Principles and Techniques of Algorithmic Differentiation 2000 Society for Industrial and Applied Mathematics Philadelphia, PA, USA
15. Y. Hida, X.S. Li, D.H. Bailey, Quad-double arithmetic:A algorithms, implementation, and application, Technical Report LBNL-46996, Department of Computer Science, University of California, Berkeley, CA, USA, October 2000.
16. Hida Y. Li X.S. Bailey D.H. Quad-double arithmetic: Algorithms, implementation, and application Burgess N. Ciminiera L. 15th IEEE Symposium on Computer Arithmetic 2001 155-162 Institute of Electrical and Electronics Engineers New York
17. Higham N.J. The accuracy of floating point summation SIAM J. Sci. Comput. 14 4 1993 783-799
18. Higham N.J. Accuracy and Stability of Numerical Algorithms 1996 Society for Industrial and Applied Mathematics Philadelphia, PA, USA
19. IEEE Computer Society, New York, IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985, reprinted in SIGPLAN Notices 22(2) 1987 (1985) 9-25.
20. Kahan W. Further remarks on reducing truncation errors Comm. ACM 8 1 1965 40
21. Kulisch U.W. Miranker W.L. Computer Arithmetic in Theory and in Practice 1981 Academic Press New York
22. Langlois P. Automatic linear correction of rounding errors BIT 41 3 2001 515-539
23. Langlois P. Nativel F. Reduction and bounding of the rounding error in floating point arithmetic C.R. Acad. Sci. Paris, Sér. 1 327 1998 781-786
24. Langlois P. Nativel F. When automatic linear correction of rounding errors is exact C.R. Acad. Sci. Paris, Sér. 1 328 1999 543-548
25. Li X.S. Demmel J.W. Bailey D.H. Henry G. Hida Y. Iskandar J. Kahan W. Kang S.Y. Kapur A. Martin M.C. Thompson B.J. Tung T. Yoo D.J. Design, implementation and testing of extended and mixed precision BLAS ACM Trans. Math. Software 28 2 2002 152-205
26. Linnainmaa S. Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms BIT 23 1983 346-359
27. Markstein P. IA-64 and Elementary Functions. Speed and Precision, Hewlett-Packard Professional Books 2000 Prentice-Hall PTR Englewood Cliffs, NJ
28. McCracken D.D. Dorn W.S. Numerical Methods and Fortran Programming: With Applications in Science and Engineering 1964 Wiley New York
29. Pichat M. Correction d'une somme en arithmétique à virgule flottante Numer. Math. 19 1972 400-406
30. M. Pichat, Contribution à l'étude des erreurs d'arrondi en arithmétique à virgule flottante, Thèse de Doctorat d'Etat, Université de Grenoble 1, Grenoble, France, 1976 (in French).
31. D.M. Priest, On properties of floating point arithmetics: Numerical stability and the cost of accurate computations, Ph.D. Thesis, Mathematics Department, University of California, Berkeley, CA, USA, November 1992. URL: ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z
32. Rall L.B. Convergence of the Newton process to multiple solutions Numer. Math. 9 1966 25-37
33. Robertazzi T.G. Schwartz S.C. Best "ordering" for floating-point addition ACM Trans. Math. Software 14 1 1988 101-110
34. Soderquist P. Leeser M. Division and square root: choosing the right implementation IEEE Micro 17 4 1997 56-66
35. Stoer J. Bulirsch R. Introduction to Numerical Analysis 2nd Edition 1993 Springer New York
36. Vignes J. A stochastic arithmetic for reliable scientific computation Math. Comput. Simulation 35 1993 233-261
37. Wilkinson J.H. Error analysis revisited IMA Bull. 22 11/12 1986 192-200