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Volumn 1432, Issue , 1998, Pages 276-287

Determinant: Old algorithms, new insights

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; LINEAR ALGEBRA; POLYNOMIALS;

EID: 84957705350     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/BFb0054375     Document Type: Conference Paper
Times cited : (2)

References (24)
  • 1
    • 0021388907 scopus 로고
    • On computing the determinant in small parallel time using a small number of processors
    • S.J. Berkowitz. On computing the determinant in small parallel time using a small number of processors. Information Processing Letters, 18:147-150, 1984.
    • (1984) Information Processing Letters , vol.18 , pp. 147-150
    • Berkowitz, S.J.1
  • 2
    • 0001217760 scopus 로고
    • A combinatorial proof of the all minors matrix theorem
    • S. Chaiken. A combinatorial proof of the all minors matrix theorem. SIAM J. Algebraic Discrete Methods, 3:319-329, 1982.
    • (1982) SIAM J. Algebraic Discrete Methods , vol.3 , pp. 319-329
    • Chaiken, S.1
  • 3
    • 85034440079 scopus 로고
    • Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic
    • Springer
    • A. L. Chistov. Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic. In Proc Int. Conf. Foundations of Computation Theory, LNCS 199, pages 63-69. Springer, 1985.
    • (1985) Proc Int. Conf. Foundations of Computation Theory, LNCS , vol.199 , pp. 63-69
    • Chistov, A.L.1
  • 4
    • 0000538288 scopus 로고
    • Fast parallel inversion algorithm
    • L. Csanky. Fast parallel inversion algorithm. SIAM J of Computing, 5:818-823, 1976.
    • (1976) SIAM J of Computing , vol.5 , pp. 818-823
    • Csanky, L.1
  • 5
    • 84957673790 scopus 로고
    • Technical Report Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin
    • C. Datum. DET=L (#L). Technical Report Informatik-Preprint 8, Fachbereich Informatik der Humboldt-Universität zu Berlin, 1991.
    • (1991) DET=L (#L)
    • Datum, C.1
  • 7
    • 0001805433 scopus 로고
    • Etude algébrique de certains problèmes d’analyse combinatoire et du calcul des probabilités
    • D. Foata. Etude algébrique de certains problèmes d’analyse combinatoire et du calcul des probabilités. Publ. Inst. Statist. Univ. Paris, 14:81-241, 1965.
    • (1965) Publ. Inst. Statist. Univ. Paris , vol.14 , pp. 81-241
    • Foata, D.1
  • 8
    • 0001755175 scopus 로고
    • A combinatorial proof of Jacobi’s identity
    • D. Foata. A combinatorial proof of Jacobi’s identity. Ann. Discrete Math., 6:125--135, 1980.
    • (1980) Ann. Discrete Math , vol.6
    • Foata, D.1
  • 10
    • 0041782158 scopus 로고
    • Tournaments and Vandermonde’s determinant
    • I. Gessel. Tournaments and Vandermonde’s determinant. J Graph Theory, 3:305-307, 1979.
    • (1979) J Graph Theory , vol.3 , pp. 305-307
    • Gessel, I.1
  • 13
    • 0040560511 scopus 로고    scopus 로고
    • Bideterminants, arborescences and extension of the matrix-tree theorem to semirings
    • M. Minoux. Bideterminants, arborescences and extension of the matrix-tree theorem to semirings. Discrete Mathematics, 171:191-200, 1997.
    • (1997) Discrete Mathematics , vol.171 , pp. 191-200
    • Minoux, M.1
  • 14
    • 0013316895 scopus 로고    scopus 로고
    • Determinant: Combinatorics, algorithms, complexity
    • 1997. A preliminary version appeared as “A combinatorial algorithm for the determinant” in Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms SODA97
    • M. Mahajan and V Vinay. Determinant: combinatorics, algorithms, complexity. Chicago Journal of Theoretical Computer Science http://cs-www.uchicago.edu/publications/cjtcs, 1997:5, 1997. A preliminary version appeared as “A combinatorial algorithm for the determinant” in Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms SODA97.
    • (1997) Chicago Journal of Theoretical Computer Science , pp. 5
    • Mahajan, M.1    Vinay, V.2
  • 15
    • 0011615213 scopus 로고
    • Line-digraphs, arborescences, and theorems of Tutte and Knuth
    • J. B. Orlin. Line-digraphs, arborescences, and theorems of Tutte and Knuth. J. Combin. Theory Set. B, 25:187-198, 1978.
    • (1978) J. Combin. Theory Set. B , vol.25 , pp. 187-198
    • Orlin, J.B.1
  • 16
    • 0006147520 scopus 로고
    • A method of determining explicitly the coefficients of the characteristic polynomial
    • P. A. Samuelson. A method of determining explicitly the coefficients of the characteristic polynomial. Ann. Math. Star., 13:424-429, 1942.
    • (1942) Ann. Math. Star , vol.13 , pp. 424-429
    • Samuelson, P.A.1
  • 18
    • 0038015710 scopus 로고
    • A combinatorial proof of the Cayley-Hamilton theorem
    • H. Straubing. A combinatorial proof of the Cayley-Hamilton theorem. Discrete Maths., 43:273-279, 1983.
    • (1983) Discrete Maths , vol.43 , pp. 273-279
    • Straubing, H.1
  • 22
    • 0003370550 scopus 로고
    • Why is boolean complexity theory difficult?
    • M. S. Paterson, editor, Cambridge University Press, London Mathematical Society Lecture Notes Series 169
    • L. G. Valiant. Why is boolean complexity theory difficult? In M. S. Paterson, editor, Boolean Function Complexity. Cambridge University Press, 1992. London Mathematical Society Lecture Notes Series 169.
    • (1992) Boolean Function Complexity
    • Valiant, L.G.1
  • 23
    • 0026375502 scopus 로고
    • Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits
    • V Vinay. Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In Proc. 6th Structure in Complexity Theory Conference, pages 270-284, 1991.
    • (1991) Proc. 6Th Structure in Complexity Theory Conference , pp. 270-284
    • Vinay, V.1
  • 24
    • 0001772282 scopus 로고
    • A combinatorial approach to matrix algebra
    • D. Zeilberger. A combinatorial approach to matrix algebra. Discrete Mathematics, 56:61-72, 1985.
    • (1985) Discrete Mathematics , vol.56 , pp. 61-72
    • Zeilberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.