An optimal, stable continued fraction algorithm for arbitrary dimension

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

Volumn 1084, Issue , 1996, Pages 31-43

  Rössner, Carsten ^a   Schnorr, Claus P ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; COMBINATORIAL OPTIMIZATION;

ARBITRARY DIMENSION; CONTINUED FRACTION ALGORITHM; DIRICHLET; REAL VECTOR; SIMULTANEOUS DIOPHANTINE APPROXIMATION;

INTEGER PROGRAMMING;

EID: 84879106319     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61310-2_3     Document Type: Conference Paper

References (20)

1. [Berg80] G. Bergman: Notes od Ferguson and Forcade's Generalized Euclidean Algorithm. TR, Department of Mathematics, University of California, Berkeley, CA, 1980.
2. [BernYl] L. Bernstein: The Jacobi-Perron Algorithm, Lecture Notes in Mathematics 207, Berlin-Heidelberg-New York (1971), pp. 1-161.
3. [BBP96] D. Bailey, P. Borwein, S. Plouffe: On the Rapid Computation of Various Polylogarithmic Constants, Technical Report, Simon Frazer University, Burnaby, B. C., Canada (1996).
4. [Di1842] G.L. Dirichlet: VeraUgemeinerung eines Satzes aus der Lehre von den Kettenbrüchen nebst einigen Anwendungen auf die Theorie der Zahien, Bericht über die zur Bekanntmachung geigneten Verhandlungen der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1842), pp. 93-95.
5. [FB92] H.R.P. Ferguson and D.H. Bailey: A Polynomial Time, Numerically Stable Integer Relation Algorithm. RNR Technical Report RNR-91-032, NASA Ames Research Center, Moffett Field, CA (1992).
6. [FF79] H. Ferguson and R. Forcade: Generalization of the Euclidean Algorithm for Real Numbers to all Dimensions Higher than Two, Bull. Amer. Math. Soc., (New Series) 1 (1979), pp. 912-914.
7. [Ge75] W.M. Gentleman: Error Analysis of QR Decomposition by Givens Transformations. Linear Algebra and its Applications, Vol. 10, pp. 189-197, 1975.
8. [GL89] G.H. Golub and C.F. van Loan: Matrix Computations. The Johns Hopkins University Press, London (1989).
9. [H95] C. HECKLER: Automatische Parallelisierung und parallele Gitterbasenreduk-tion. Ph.D. Thesis, University of Saarbrücken, 1995.
10. [HT93] C. Heckler and L. Thiele: A Parallel Lattice Basis Reduction for Mesh-connected Processor Arrays and Parallel Complexity. Proceedings of the 5th Symposium on Parallel and Distributed Processing, Dallas (1993).
11. [HJLS89] J. Hastad, B. Just, J.C. Lagarias and C.P. Schnorr: Polynomial Time Algorithms for Finding Integer Relations among Real Numbers. SIAM J, Comput., Vol. 18, No. 5 (1989), pp. 859-881.
12. [Jal868] C.G.J. Jacobi: Allgemeine Theorie der Kettenbruchähnlichen Algorithmen, J. Reine Angew. Math. 69 (1868), pp. 29-64.
13. [Jo93] A. Joux: A Fast Parallel Lattice Basis Reduction Algorithm. Proceedings of the 2nd Gauss Symposium, Munich (1993).
14. [Ju92] B. Just: Generalizing the Continued Fraction Algorithm to Arbitrary Dimensions. SIAM J. Comput., Vol. 21, No. 5 (1992), pp. 909-926.
15. [LLL82] A.K. Lenstra, H.W. Lenstra, Jr. and L. Lovász: Factoring Polynomials with Rational Coefficients. Math. Ann. 21 (1982), pp. 515-534.
16. [Pel907] O. Perron: Grundlagen fíír eine Theorie des Jacobischen Kettenbruchalgo-rithmus. Math. Ann. 64 (1907), pp. 1-76.
17. [RS95] C. Rössner and C.P. Schnorr: Computation of Highly Regular Nearby Points. Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems, Tel Aviv (1995).
18. [Sc94] C.P. Schnorr: Block Reduced Lattice and Successive Minima. Combinatorics, Probablity and Computing 3 (1994), pp. 507-522.
19. [Sz70] G. Szekeres: Multidimensional Continued Fractions. Ann. Univ. Sci. Budapest, Edtvos Sect. Math. 13 (1970), pp. 113-140.
20. [Wi65] J.H. WILKINSON: The Algebraic Eigenvalue Problem. Oxford University Press (1965).