메뉴 건너뛰기




Volumn 12, Issue 4, 1999, Pages 474-490

Determinant: Old algorithms, new insights

Author keywords

Algorithms; Combinatorics; Determinant; Graphs; Matrices

Indexed keywords


EID: 0000482972     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480198338827     Document Type: Article
Times cited : (23)

References (27)
  • 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. Inform. Process Lett., 18 (1984), pp. 147-150.
    • (1984) Inform. Process Lett. , vol.18 , pp. 147-150
    • Berkowitz, S.J.1
  • 2
    • 1842653674 scopus 로고
    • The many facets of combinatorial matrix theory
    • C. R. Johnson, ed., AMS, Providence, RI
    • R. A. BRUALDI, The many facets of combinatorial matrix theory, in Matrix Theory and Applications, C. R. Johnson, ed., AMS, Providence, RI, 1990, pp. 1-35.
    • (1990) Matrix Theory and Applications , pp. 1-35
    • Brualdi, R.A.1
  • 4
    • 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. Alg. Discrete Methods, 3 (1982), pp. 319-329.
    • (1982) SIAM J. Alg. Discrete Methods , vol.3 , pp. 319-329
    • Chaiken, S.1
  • 5
    • 85034440079 scopus 로고
    • Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic
    • Proc. Int. Conf. Foundations of Computation Theory, Springer-Verlag, New York, Berlin
    • 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, Lecture Notes in Comput. Sci. 199, Springer-Verlag, New York, Berlin, 1985, pp. 63-69
    • (1985) Lecture Notes in Comput. Sci. 199 , pp. 63-69
    • Chistov, A.L.1
  • 6
    • 0000538288 scopus 로고
    • Fast parallel inversion algorithm
    • L. CSANKY, Fast parallel inversion algorithm. SIAM J. Comput., 5 (1976), pp. 618-623.
    • (1976) SIAM J. Comput. , vol.5 , pp. 618-623
    • Csanky, L.1
  • 7
    • 0038585401 scopus 로고
    • preprint 8 Fachbereich Informatik der Humboldt-Universität zu Berlin, Informatik
    • (#L), preprint 8 Fachbereich Informatik der Humboldt-Universität zu Berlin, Informatik, 1991.
    • (1991) (#L)
    • Damm, C.1
  • 8
    • 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 (1965), pp. 81-241.
    • (1965) Publ. Inst Statist. Univ. Paris , vol.14 , pp. 81-241
    • Foata, D.1
  • 9
    • 0001755175 scopus 로고
    • A combinatorial proof of Jacobi's identity
    • D. FOATA, A combinatorial proof of Jacobi's identity, Ann. Discrete Math., 6 (1980), pp. 125-135.
    • (1980) Ann. Discrete Math. , vol.6 , pp. 125-135
    • Foata, D.1
  • 12
    • 0041782158 scopus 로고
    • Tournaments and Vandermonde's determinant
    • I. GESSEL, Tournaments and Vandermonde's determinant, J. Graph Theory, 3 (1979), pp. 305-307.
    • (1979) J. Graph Theory , vol.3 , pp. 305-307
    • Gessel, I.1
  • 16
    • 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 Math., 171 (1997), pp. 191-200.
    • (1997) Discrete Math. , vol.171 , pp. 191-200
    • Minoux, M.1
  • 17
    • 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 Ser. B, 25 (1978) pp. 187-198.
    • (1978) J. Combin. Theory Ser. B , vol.25 , pp. 187-198
    • Orlin, J.B.1
  • 18
    • 84973993463 scopus 로고
    • The Cayley-Hamilton theorem for semirings
    • D. E. RUTHERFORD, The Cayley-Hamilton theorem for semirings, Proc. Roy. Soc. Edinburgh Sect A, 66 (1964), pp. 211-215.
    • (1964) Proc. Roy. Soc. Edinburgh Sect A , vol.66 , pp. 211-215
    • Rutherford, D.E.1
  • 19
    • 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. Stat., 13 (1942) pp. 424-429.
    • (1942) Ann. Math. Stat. , vol.13 , pp. 424-429
    • Samuelson, P.A.1
  • 20
    • 84961475121 scopus 로고
    • Vermeidung von divisionen
    • V. STRASSEN, Vermeidung von divisionen, J. Reine Angew Math , 264 (1973), pp. 182-202.
    • (1973) J. Reine Angew Math , vol.264 , pp. 182-202
    • Strassen, V.1
  • 21
    • 0038015710 scopus 로고
    • A combinatorial proof of the Cayley-Hamilton theorem
    • H. STRAUBING, A combinatorial proof of the Cayley-Hamilton theorem, Discrete Math., 43 (1983), pp. 273-279.
    • (1983) Discrete Math. , vol.43 , pp. 273-279
    • Straubing, H.1
  • 25
    • 0003370550 scopus 로고
    • Why is Boolean complexity theory difficult?
    • M. S. Paterson, ed., London Math. Soc. Lecture Notes Ser. 169, Cambridge University Press, Cambridge, UK
    • L. G. VALIANT, Why is Boolean complexity theory difficult?, in Boolean Function Complexity, M. S. Paterson, ed., London Math. Soc. Lecture Notes Ser. 169, Cambridge University Press, Cambridge, UK, 1992, pp. 84-94.
    • (1992) Boolean Function Complexity , pp. 84-94
    • Valiant, L.G.1
  • 27
    • 0001772282 scopus 로고
    • A combinatorial approach to matrix algebra
    • D. ZEILBERGER, A combinatorial approach to matrix algebra. Discrete Math., 56 (1985), pp. 61-72.
    • (1985) Discrete Math. , vol.56 , pp. 61-72
    • Zeilberger, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.