A comparative study of algorithms for computing continued fractions of algebraic numbers

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1122, Issue , 1996, Pages 35-48

  Brent, Richard P ^a   van der Poorten, Alfred J ^b   te Riele, Herman J J ^c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b MACQUARIE UNIVERSITY   (Australia)

^c CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84958063314     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61581-4_39     Document Type: Conference Paper

References (16)

1. Richard P. Brent and Edwin M. McMillan, 'Some new algorithms for high-precision computation of Euler's constant', Math. Comp. 34 (1980), 305-312.
2. Enrico Bombieri and Alfred J. van der Poorten, 'Continued fractions of algebraic numbers', in Computational Algebra and Number Theory, Sydney 1992, Wieb Bosma and Alf van der Poorten eds., (Kluwer, 1995), 137-152.
3. David G. Cantor, Paul G. Galyean and Horst G. Zimmer, 'A continued fraction algorithm for real algebraic numbers', Math. Comp. 26 (1972), 785-791.
4. A. Khintchine, 'Metrische Kettenbruchprobleme', Compositio Math. 1 (1935), 361-382.
5. Donald E. Knuth, The Art of Computer Programming, Volume 2, Seminumerical Algorithms, (Reading, Mass.: Addison-Wesley, Second Edition, 1981).
6. Serge Lang and Hale Trotter, 'Continued fractions for some algebraic numbers', J. reine angew. Math., 255 (1972), 112-134.
7. D. H. Lehmer, 'Euclid's algorithm for large numbers', Amer. Math. Monthly, 45 (1983), 227-233.
8. P. Lévy, 'Sur le d@veloppement en fraction continue d'un nombre choisi au hasard', Compositio Math. 3 (1936), 286-303.
9. Gustav Lochs, 'Die ersten 968 Kettenbruchnenner von 7r', Monatsh. Math., 67 (1963), 311-316.
10. Gustav Lochs, 'Vergleich der Genauichkeit von Dezimalbruch und Kettenbruch', Abh. Math. Seminar Hamburg, 27 (1964), 142-144.
11. Attila Pethő, 'On the resolution of Thue inequalities', J. Symb. Comp. 4 (1987), 103-109.
12. R. D. Richtmyer, Marjorie Devaney and N. Metropolis, 'Continued fraction expansions of algebraic numbers', Numer. Math. 4 (1962), 68-84.
13. A. SchSnhage, 'Schnelle Berechnung von Kettenbruchentwicklungen', Acta Informatiea 1 (1971), 139-144
14. P. Shiu, 'Computation of continued fractions without input values', Math. Comp. 64 (1995), 1307-1317.
15. H. M. Stark, 'An explanation of some exotic continued fractions found by Brillhart', in Computers in Number Theory, A. O. L. Atkin and B. J. Birch eds., (Academic Press, 1971), 21-35.
16. Benjamin M.M. de Weger, Complete solution of a Thue inequality, Technical Report 9561/B, December 15, 1995, Econometric Institute, Erasmus University Rotterdam.