A new algorithm and refined bounds for extended gcd computation

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

Volumn 1122, Issue , 1996, Pages 145-150

  Ford, David ^a   Havas, George ^b  

^a Gina Cody School of Engineering and Computer Science   (Canada)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; NUMBER THEORY;

ALGORITHM FOR SOLVING;

ALGORITHMS;

EID: 77954700862     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61581-4_50     Document Type: Conference Paper

References (14)

1. W.A. Blankinship. A new version of the Euclidean algorithm. Amer. Math. Mon., 70:742-745, 1963.
2. G.H. Bradley. Algorithm and bound for the greatest common divisor of n integers. Commun. ACM, 13:433-436, 1970.
3. G. Havas and B.S. Majewski. Integer matrix diagonalization. J. Symbolic Comput., to appear.
4. G. Havas and B.S. Majewski. Hermite normal form computation for integer matrices. Congressus Numerantium, 105:184-193, 1994.
5. G. Havas and B.S. Majewski. A hard problem which is almost always easy. In Algorithms and Computation, Lecture Notes in Computer Science 1004, 216-223, 1995.
6. G. Havas, B.S. Majewski and K.R. Matthews. Extended gcd algorithms. Technical Report TR0302, The University of Queensland, Brisbane, 1994.
7. C.S. Iliopoulos. Worst case complexity bounds on algorithms for computing the canonical structure of finite abelian groups and the Hermite and Smith normal forms of an integer matrix. SIAM J. Computing, 18:658-669, 1989.
8. D.E. Knuth. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms. Addison-Wesley, Reading, Mass., 2nd edition, 1973.
9. B.S. Majewski and G. Havas. The complexity of greatest common divisor computations. In Algorithmic Number Theory, Lecture Notes in Computer Science 877, 184-193, 1994.
10. B.S. Majewski and G. Havas. A solution to the extended gcd problem. In ISSAC'95 (Proc. 1995 Internat. Sympos. Symbolic Algebraic Comput.), ACM Press, New York, 248-253, 1995.
11. B.S. Majewski and G. Havas. Extended gcd calculation. Congressus Numerantium, 111:104-114, 1995.
12. M-H. Mathieu and D. Ford. On p-adic Computation of the Rational Form of a Matrix, J. Symbolic Comput., 10:453-464, 1990.
13. P. Ozello. Calcul Exact des formes de Jordan et de Frobenius d'une Matrice. Doctoral Thesis, University of Grenoble, 1987.
14. M.S. Waterman. Multidimensional greatest common divisor and Lehmer algorithms. BIT, 17:465-478, 1977.