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Volumn 161, Issue 1-2, 1996, Pages 69-92

Algorithmes de calcul de la réduction de Hermite d'une matrice à coefficients polynomiaux

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; LINEAR ALGEBRA; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS;

EID: 0030181767     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00090-9     Document Type: Article
Times cited : (7)

References (23)
  • 1
    • 84968497774 scopus 로고
    • Sylvester's identity and multistep integer-preserving Gaussian elimination
    • E.H. Bareiss, Sylvester's identity and multistep integer-preserving Gaussian elimination, Math. Comp. 22 (1968) 565-578.
    • (1968) Math. Comp. , vol.22 , pp. 565-578
    • Bareiss, E.H.1
  • 2
    • 0021388907 scopus 로고
    • On computing the determinant in small parallel time using a small number of processors
    • S.J. Berkovitz, On computing the determinant in small parallel time using a small number of processors, Inform. Process. Lett. 18 (3) (1984) 147-150.
    • (1984) Inform. Process. Lett. , vol.18 , Issue.3 , pp. 147-150
    • Berkovitz, S.J.1
  • 3
    • 0000205195 scopus 로고
    • Algorithms for the solution of systems of linear diophantine equations
    • T.-W. Chou and G. Collins, Algorithms for the solution of systems of linear diophantine equations, SIAM J. Comput. 11 (1982) 687-708.
    • (1982) SIAM J. Comput. , vol.11 , pp. 687-708
    • Chou, T.-W.1    Collins, G.2
  • 4
    • 0002419721 scopus 로고
    • Algebraic extensions and algebraic closure in Scratchpad
    • Lecture Notes in Computer Science, Springer, Berlin
    • C. Dicrescenzo and D. Duval, Algebraic extensions and algebraic closure in Scratchpad, in: Symbolic and Algebraic Computaton (ISSAC 88), Lecture Notes in Computer Science, Vol. 358 (Springer, Berlin, 1989) 440-444.
    • (1989) Symbolic and Algebraic Computaton (ISSAC 88) , vol.358 , pp. 440-444
    • Dicrescenzo, C.1    Duval, D.2
  • 5
    • 85025486043 scopus 로고
    • About a new method for computing in algebraic number fields
    • Lecture Notes in Computer Science, Springer, Berlin
    • J. Dora, C. Dicrescenzo and D. Duval, About a new method for computing in algebraic number fields, Proc. Eurocal '85, Lecture Notes in Computer Science, Vol. 204 (Springer, Berlin, 1985) 289-290.
    • (1985) Proc. Eurocal '85 , vol.204 , pp. 289-290
    • Dora, J.1    Dicrescenzo, C.2    Duval, D.3
  • 6
    • 0023294681 scopus 로고
    • Hermite normal form computation using modulo determinant arithmetic
    • D. Domich, R. Kannan and L. Trotten, Hermite normal form computation using modulo determinant arithmetic, Math. Oper. Res. 12 (1987) 50-59.
    • (1987) Math. Oper. Res. , vol.12 , pp. 50-59
    • Domich, D.1    Kannan, R.2    Trotten, L.3
  • 7
    • 0010954098 scopus 로고
    • An application of modular arithmetic to the construction of algorithms solving systems of linear equations
    • M. Frumkin, An application of modular arithmetic to the construction of algorithms solving systems of linear equations, Soviet. Math. Dokl. 17 (1976) 1165-1169.
    • (1976) Soviet. Math. Dokl. , vol.17 , pp. 1165-1169
    • Frumkin, M.1
  • 8
    • 84964043305 scopus 로고
    • Polynomial time algorithms in the theory of linear diophantine equations
    • M. Karpinsky, eds., Springer, Berlin
    • M. Frumkin, Polynomial time algorithms in the theory of linear diophantine equations, in: M. Karpinsky, eds., Fundamentals of Computation Theory, Lecture Notes in Computer Science, Vol. 56 (Springer, Berlin, 1977) 386-392.
    • (1977) Fundamentals of Computation Theory, Lecture Notes in Computer Science, Vol. 56 , vol.56 , pp. 386-392
    • Frumkin, M.1
  • 9
    • 0002989595 scopus 로고
    • Complexity questions in number theory
    • M. Frumkin, Complexity questions in number theory, J. Soviet. Math. 29 (1985) 386-392.
    • (1985) J. Soviet. Math. , vol.29 , pp. 386-392
    • Frumkin, M.1
  • 10
    • 0001173498 scopus 로고
    • Spécialisation de la suite de Sturm et sous-résultants. 1
    • version plus détaillée, dans CALSYF journées du GRECO de Calcul Formel, 1989
    • L. Gonzalez, H. Lombardi, T. Recio and M.F. Roy, Spécialisation de la suite de Sturm et sous-résultants. 1, RAIRO Inform. Théor. Appl. 24 (1990) 561-588 (version plus détaillée, dans CALSYF journées du GRECO de Calcul Formel, 1989).
    • (1990) RAIRO Inform. Théor. Appl. , vol.24 , pp. 561-588
    • Gonzalez, L.1    Lombardi, H.2    Recio, T.3    Roy, M.F.4
  • 11
    • 0026403469 scopus 로고
    • Asymptotically fast triangularization of matrices over rings
    • J. Hafner and K. McCurley, Asymptotically fast triangularization of matrices over rings, SIAM J. Comput. 20 (1991) 1068-1083.
    • (1991) SIAM J. Comput. , vol.20 , pp. 1068-1083
    • Hafner, J.1    McCurley, K.2
  • 12
    • 0024716132 scopus 로고
    • 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 matrice
    • C. 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 matrice, SIAM J. Comput. 18 (1989) 658-669.
    • (1989) SIAM J. Comput. , vol.18 , pp. 658-669
    • Iliopoulos, C.1
  • 13
    • 0024716008 scopus 로고
    • Worst-case complexity bounds on algorithms for computing the canonical structure of infinite abelian groups and solving systems of linear diophantine equations
    • C. Iliopoulos, Worst-case complexity bounds on algorithms for computing the canonical structure of infinite abelian groups and solving systems of linear diophantine equations, SIAM J. Comput. 18 (1989) 670-678.
    • (1989) SIAM J. Comput. , vol.18 , pp. 670-678
    • Iliopoulos, C.1
  • 14
    • 0020784938 scopus 로고
    • Solving systems of linear equations over polynomials
    • R. Kannan, Solving systems of linear equations over polynomials, Theoret. Comput. Sci. 39 (1985) 69-88.
    • (1985) Theoret. Comput. Sci. , vol.39 , pp. 69-88
    • Kannan, R.1
  • 15
    • 0001047308 scopus 로고
    • Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix
    • R. Kannan and A. Bachem, Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix, SIAM J. Comput. 8 (1979) 499-507.
    • (1979) SIAM J. Comput. , vol.8 , pp. 499-507
    • Kannan, R.1    Bachem, A.2
  • 19
    • 0006147520 scopus 로고
    • A method for determining explicitly the coefficients of the characteristic equation
    • P.A. Samuelson, A method for determining explicitly the coefficients of the characteristic equation, Ann. Math. Statist. 13 (1942) 424-429.
    • (1942) Ann. Math. Statist. , vol.13 , pp. 424-429
    • Samuelson, P.A.1
  • 22
    • 0347293697 scopus 로고
    • Computation of Smith normal forms of polynomial mltrices
    • Kiev, Ukraine ACM Press, New York
    • G. Villard, Computation of Smith normal forms of polynomial mltrices, dans Internat. Symp. on Symbolic and Algebraic Computation, Kiev, Ukraine (ACM Press, New York, 1993) 209-217.
    • (1993) Internat. Symp. on Symbolic and Algebraic Computation , pp. 209-217
    • Villard, G.1
  • 23
    • 0347293699 scopus 로고    scopus 로고
    • Generalized subresultants for computing the Smith normal form of polynomial matrices
    • à paraître
    • G. Villard, Generalized subresultants for computing the Smith normal form of polynomial matrices, J. Symbolic Comput. à paraître.
    • J. Symbolic Comput.
    • Villard, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.