메뉴 건너뛰기




Volumn 9, Issue 2, 2000, Pages 73-112

Lower bounds for the bilinear complexity of associative algebras

Author keywords

Associative algebras; Bilinear complexity; Lower bound; Matrix multiplication; Rank; Substitution method

Indexed keywords


EID: 0034557785     PISSN: 10163328     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001605     Document Type: Article
Times cited : (17)

References (27)
  • 1
    • 0001245248 scopus 로고
    • On the algorithmic complexity of associative algebras
    • A. ALDER & V. STRASSEN (1981). On the algorithmic complexity of associative algebras. Theoret. Comput. Sci. 15, 201-211.
    • (1981) Theoret. Comput. Sci. , vol.15 , pp. 201-211
    • Alder, A.1    Strassen, V.2
  • 4
    • 0040531570 scopus 로고    scopus 로고
    • Lower bounds for the multiplicative complexity of matrix multiplication
    • M. BLÄSER (1999b). Lower bounds for the multiplicative complexity of matrix multiplication. Comput. Complexity 8, 203-226.
    • (1999) Comput. Complexity , vol.8 , pp. 203-226
    • Bläser, M.1
  • 6
    • 0002125925 scopus 로고
    • On the optimal evaluation of a set of bilinear forms
    • R. W. BROCKETT & D. DOBKIN (1978). On the optimal evaluation of a set of bilinear forms. Linear Algebra Appl. 19, 207-235.
    • (1978) Linear Algebra Appl. , vol.19 , pp. 207-235
    • Brockett, R.W.1    Dobkin, D.2
  • 7
    • 0024715662 scopus 로고
    • A lower bound for matrix multiplication
    • N. H. BSHOUTY (1989). A lower bound for matrix multiplication. SIAM J. Comput. 18, 759-765.
    • (1989) SIAM J. Comput. , vol.18 , pp. 759-765
    • Bshouty, N.H.1
  • 8
    • 0009597713 scopus 로고
    • On a class of primary algebras of minimal rank
    • W. BÜCHI & M. CLAUSEN (1985). On a class of primary algebras of minimal rank. Linear Algebra Appl. 69, 249-268.
    • (1985) Linear Algebra Appl. , vol.69 , pp. 249-268
    • Büchi, W.1    Clausen, M.2
  • 10
    • 0003956966 scopus 로고
    • Wiley
    • P. M. COHN (1991). Algebra, volume 3. Wiley.
    • (1991) Algebra , vol.3
    • Cohn, P.M.1
  • 12
    • 0013166688 scopus 로고
    • On the varieties of optimal algorithms for the computation of bilinear mappings: The isotropy group of a bilinear mapping
    • H. F. DE GROOTE (1978). On the varieties of optimal algorithms for the computation of bilinear mappings: The isotropy group of a bilinear mapping. Theoret. Comput. Sci. 7, 1-24.
    • (1978) Theoret. Comput. Sci. , vol.7 , pp. 1-24
    • De Groote, H.F.1
  • 13
    • 0009616563 scopus 로고
    • Characterization of division algebras of minimal rank and the structure of their algorithm varieties
    • H. F. DE GROOTE (1983). Characterization of division algebras of minimal rank and the structure of their algorithm varieties. SIAM J. Comput. 12, 101-117.
    • (1983) SIAM J. Comput. , vol.12 , pp. 101-117
    • De Groote, H.F.1
  • 14
    • 0004116402 scopus 로고
    • Lectures on the complexity of bilinear problems
    • Springer
    • H. F. DE GROOTE (1986). Lectures on the Complexity of Bilinear Problems. Lecture Notes in Comput. Sci. 245, Springer.
    • (1986) Lecture Notes in Comput. Sci. , vol.245
    • De Groote, H.F.1
  • 15
  • 16
    • 0022059784 scopus 로고
    • On the multiplicative complexity of modules over associative algebras
    • W. HARTMANN (1985). On the multiplicative complexity of modules over associative algebras. SIAM J. Comput. 14, 383-395.
    • (1985) SIAM J. Comput. , vol.14 , pp. 383-395
    • Hartmann, W.1
  • 17
    • 84974699592 scopus 로고
    • On associative algebras of minimal rank
    • Proceedings of the AAECC 2, Springer
    • J. HEINTZ & J. MORGENSTERN (1986). On associative algebras of minimal rank. In Proceedings of the AAECC 2, Lecture Notes in Comput. Sci. 228, Springer, 1-24.
    • (1986) Lecture Notes in Comput. Sci. , vol.228 , pp. 1-24
    • Heintz, J.1    Morgenstern, J.2
  • 18
    • 0004293970 scopus 로고
    • Interscience Publishers, 3rd edition
    • N. JACOBSON (1966). Lie Algebras. Interscience Publishers, 3rd edition.
    • (1966) Lie Algebras
    • Jacobson, N.1
  • 20
    • 0000238829 scopus 로고
    • Methods for computing values of polynomials
    • V. PAN (1966). Methods for computing values of polynomials. Russian Math. Surveys 21, 105-136.
    • (1966) Russian Math. Surveys , vol.21 , pp. 105-136
    • Pan, V.1
  • 22
    • 34250487811 scopus 로고
    • Gaussian elimination is not optimal
    • V. STRASSEN (1969). Gaussian elimination is not optimal. Numer. Math. 13, 354-356.
    • (1969) Numer. Math. , vol.13 , pp. 354-356
    • Strassen, V.1
  • 23
    • 0039957423 scopus 로고
    • Rank and optimal computation of generic tensors
    • V. STRASSEN (1983). Rank and optimal computation of generic tensors. Linear Algebra Appl. 52/53, 645-685.
    • (1983) Linear Algebra Appl. , vol.52-53 , pp. 645-685
    • Strassen, V.1
  • 27
    • 0001490370 scopus 로고
    • On multiplication in algebraic extension fields
    • S. WINOGRAD (1979). On multiplication in algebraic extension fields. Theoret. Comput. Sci. 8, 359-377.
    • (1979) Theoret. Comput. Sci. , vol.8 , pp. 359-377
    • Winograd, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.