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

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.

   Google Scholar 

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.

   Google Scholar 

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.

   Google Scholar 

4. A. Khintchine, ‘Metrische Kettenbruchprobleme', Compositio Math. 1 (1935), 361–382.

   Google Scholar 

5. Donald E. Knuth, The Art of Computer Programming, Volume 2, Seminumerical Algorithms, (Reading, Mass.: Addison-Wesley, Second Edition, 1981).

   Google Scholar 

6. Serge Lang and Hale Trotter, ‘Continued fractions for some algebraic numbers', J. reine angew. Math., 255 (1972), 112–134.

   Google Scholar 

7. D. H. Lehmer, ‘Euclid's algorithm for large numbers', Amer. Math. Monthly, 45 (1983), 227–233.

   Google Scholar 

8. P. Lévy, ‘Sur le développement en fraction continue d'un nombre choisi au hasard', Compositio Math. 3 (1936), 286–303.

   Google Scholar 

9. Gustav Lochs, ‘Die ersten 968 Kettenbruchnenner von π', Monatsh. Math., 67 (1963), 311–316.

   Google Scholar 

10. Gustav Lochs, ‘Vergleich der Genauichkeit von Dezimalbruch und Kettenbruch', Abh. Math. Seminar Hamburg, 27 (1964), 142–144.

    Google Scholar 

11. Attila Pethó, ‘On the resolution of Thue inequalities', J. Symb. Comp. 4 (1987), 103–109.

    Google Scholar 

12. R. D. Richtmyer, Marjorie Devaney and N. Metropolis, ‘Continued fraction expansionsm of algebraic numbers', Numer. Math. 4 (1962), 68–84.

    Google Scholar 

13. A. Schönhage, ‘Schnelle Berechnung von Kettenbruchentwicklungen', Acta Informatica 1 (1971), 139–144

    Google Scholar 

14. P. Shiu, ‘Computation of continued fractions without input values', Math. Comp. 64 (1995), 1307–1317.

    Google Scholar 

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.

    Google Scholar 

16. Benjamin M.M. de Weger, Complete solution of a Thue inequality, Technical Report 9561/B, December 15, 1995, Econometric Institute, Erasmus University Rotterdam.

    Google Scholar 

Download references