Interval Newton iteration in multiple precision for the univariate case

Numerical Algorithms

Volumn 34, Issue 2-4, 2003, Pages 417-426

  Revol, N ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

Arbitrary accuracy; Automatic adaptation of the precision; Interval Newton algorithm; Multiple precision interval arithmetic

Indexed keywords

EID: 4043063627     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000005354.92791.41     Document Type: Article

References (21)

1. O. Aberth, Precise Numerical Methods Using C++ (Academic Press, 1998).
2. O. Aberth and M.J. Schaefer, Precise computation using range arithmetic, via C++, ACM Trans. Math. Software 18(4) (1992) 481-491.
3. G. Alefeld and J. Herzberger, Introduction to Interval Analysis (Academic Press, 1983).
4. G. Alefeld and F. Potra, A new class of interval methods with higher order of convergence, Computing 42(1) (1989) 69-80.
5. R.P. Brent, A Fortran multiple-precision arithmetic package, ACM Trans. Math. Software 4 (1978) 57-70.
6. CANT Research Group, Arithmos: A reliable integrated computational environment, University of Antwerpen, Belgium, http://win-www.uia.ac.be/u/cant/ arithmos (2001).
7. A. Connell and R. Corless, An experimental interval arithmetic package in Maple, in: Numer Analysis with Automatic Result Verification (1993).
8. I. Geulig and W. Krämer, Intervallrechnung in Maple - Die Erweiterung intpakX zum Paket intpak der Share-Library, Technical Report 99/2, Universität Karlsruhe (1999).
9. E. Hansen, Global Optimization Using Interval Analysis (Dekker, 1992).
10. E. Hansen and R.I. Greenberg, An interval Newton method, J. Appl. Math. Comput. 12 (1983) 89-98.
11. N. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed. (SIAM, Philadelphia, PA, 2002).
12. R.B. Kearfott, Empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems, SIAM J. Sci. Comput. 18(2) (1997) 574-594.
13. R.B. Kearfott and G.W. Walster, On stopping criteria in verified nonlinear systems or optimization algorithms, ACM Trans. Math. Software 26(3) (2000) 373-389.
14. J. Keiper, Interval arithmetic in Mathematica, Interval Computations (3) (1993).
15. R. Klatte, U. Kulisch, C. Lawo, M. Rauch and A. Wiethoff, C-XSC a C++ Class Library for Extended Scientific Computing (Springer, Berlin, 1993).
16. W. Krämer, U. Kulisch and R. Lohner, Numerical Toolbox for Verified Computing II, in: Advanced Numerical Problems (1998), to appear.
17. P. Langlois and N. Revol, Validating polynomial numerical computations with complementary automatic methods, RR 2001-18, LIP, École Normale Supérieure de Lyon, http://www.ens-lyon.fr/LIP/Pub/rr2001.html (2001).
18. A. Neumaier, Interval Methods for Systems of Equations (Cambridge Univ. Press, Cambridge, 1990).
19. S. Rump, Fast and parallel interval arithmetic, BIT 39(3) (1999) 534-554.
20. G.W. Stewart, What is rounding error? http://www.cs.umd.edu/-stewart,in/ pub/misc (2000).
21. J.M. Yohe, Portable software for interval arithmetic, Computing, Suppl. 2 (1980) 211-229.