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Volumn 356 LNCS, Issue , 1989, Pages 269-300

On the computational complexity of polynomials and bilinear mappings. A survey

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EID: 0001365155     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-51082-6_85     Document Type: Conference Paper
Times cited : (27)

References (58)
  • 1
    • 0001245248 scopus 로고
    • On the algorithmic complexity of associative algebras (1981)
    • Alder, A. & Strassen, V. On the algorithmic complexity of associative algebras (1981) Theoret. Comput. Sci 15 (1981) 201-211.
    • (1981) Theoret. Comput. Sci , vol.15 , pp. 201-211
    • Alder, A.1    Strassen, V.2
  • 3
    • 0005478995 scopus 로고
    • The complexity of partial derivatives (1982)
    • Baur, W. & Strassen, V. The complexity of partial derivatives (1982) Theoret. Comput. Sci. 22 (1982) 317-330.
    • (1982) Theoret. Comput. Sci , vol.22 , pp. 317-330
    • Baur, W.1    Strassen, V.2
  • 4
    • 57949087049 scopus 로고
    • Evaluation of polynomials of one variable with preliminary processing of the coefficients (1961)
    • Belaga, E.G. Evaluation of polynomials of one variable with preliminary processing of the coefficients (1961) Problemy Kibernetiki 5 (1961) 7-15.
    • (1961) Problemy Kibernetiki , vol.5 , pp. 7-15
    • Belaga, E.G.1
  • 8
    • 0010999635 scopus 로고
    • On the asymptotic complexcity of matrix multiplication (1982)
    • Coppersmith, D. & Winograd, S. On the asymptotic complexcity of matrix multiplication (1982) SIAM J. Comput. 11 (1982) 472-492.
    • (1982) SIAM J. Comput , vol.11 , pp. 472-492
    • Coppersmith, D.1    Winograd, S.2
  • 10
    • 0346393539 scopus 로고
    • On systems of bilinear forms whose minimal divisor-free algorithms are all bilinear (1961)
    • Feig, E. On systems of bilinear forms whose minimal divisor-free algorithms are all bilinear (1961) J. of Algorithms 2 (1981) 261-281.
    • (1981) J. Of Algorithms , vol.2 , pp. 261-281
    • Feig, E.1
  • 13
    • 0347023627 scopus 로고
    • Algebras having linear multiplicative complexity (1977
    • Fiduccia, C. & Zalcstein, I. Algebras having linear multiplicative complexity (1977) J. of the ACM 24 (1977) 311-331.
    • (1977) J. Of the ACM , vol.24 , pp. 311-331
    • Fiduccia, C.1    Zalcstein, I.2
  • 14
    • 84983616845 scopus 로고
    • Some polynomials that are hard to compute (1980)
    • von zur Gathen, J. & Strassen, V. Some polynomials that are hard to compute (1980) Theoret. Comput. Sci. 11-3 (1980) 331-336.
    • (1980) Theoret. Comput. Sci , vol.11 , Issue.3 , pp. 331-336
    • Von Zur Gathen, J.1    Strassen, V.2
  • 15
    • 85034755472 scopus 로고    scopus 로고
    • Ph.-D. thesis, Universidad Buenos Aires
    • Giraldo, L.E. Ph.-D. thesis, Universidad Buenos Aires.
    • Giraldo, L.E.1
  • 16
    • 0041320344 scopus 로고
    • Notes of Scientific Seminars of LOMI
    • Grigor' ev, D.Yu. Notes of Scientific Seminars of LOMI 118 (1982) 25-82.
    • (1982) , vol.118 , pp. 25-82
    • Yu Grigor' ev, D.1
  • 17
    • 0013166688 scopus 로고
    • On varieties of optimal algorithms for the computation of bilinear mappings. I. The isotropy group of a bilinear mapping (1978 (a))
    • de Groote, H.F. On varieties of optimal algorithms for the computation of bilinear mappings. I. The isotropy group of a bilinear mapping (1978 (a)) Theoret. Comput, Sci. 7 (1976) 1-24.
    • (1976) Theoret. Comput, Sci , vol.7 , pp. 1-24
    • De Groote, H.F.1
  • 18
    • 0013159451 scopus 로고
    • On varieties o jr optimal algorithms ]or the computation o] bilinear mappings, II. Optimal algorithms for 2 z 2- matri multiplication (1978 (b))
    • de Groote, H.F. On varieties o jr optimal algorithms ]or the computation o] bilinear mappings, II. Optimal algorithms for 2 z 2- matri multiplication (1978 (b)) Theoret. Comput. Sci. 7 (1978) 127-148.
    • (1978) Theoret. Comput. Sci , vol.7 , pp. 127-148
    • De Groote, H.F.1
  • 19
    • 0009616563 scopus 로고
    • Characterization of division algebras of minimal rank and the structure of their algorithms varieties (1983
    • de Groote, H.F. Characterization of division algebras of minimal rank and the structure of their algorithms varieties (1983) SIAM J. of Comput. 12-1 (1983) 101-117.
    • (1983) SIAM J. Of Comput , vol.12 , Issue.1 , pp. 101-117
    • De Groote, H.F.1
  • 20
    • 0004116402 scopus 로고
    • Lectures on the complexity of bilinear problems (1987)
    • Springer, Berlin Heidelberg
    • de Groote, H.F. Lectures on the complexity of bilinear problems (1987) LN Comput. Sci. 245, Springer, Berlin Heidelberg (1987).
    • (1987) LN Comput. Sci , vol.245
    • De Groote, H.F.1
  • 22
    • 85032229060 scopus 로고
    • A lower bound ]or the bilinear complexity of some semisimple Liealgebras (1985)
    • Proceedings of the AAECC-3 Conference, Grenoble 1985, Springer, Berlin Heidelberg
    • de Groote, H.F. & Heintz, J. A lower bound ]or the bilinear complexity of some semisimple Liealgebras (1985) in: Proceedings of the AAECC-3 Conference, Grenoble 1985. LN Comput. Sci. 229, Springer, Berlin Heidelberg (1987) 211-222.
    • (1987) LN Comput. Sci , vol.229 , pp. 211-222
    • De Groote, H.F.1    Heintz, J.2
  • 23
    • 0000627865 scopus 로고
    • Definability and -fast quantifier elimination in algebraically closed fields (1983 (a))
    • Ph.-D. thesis, Universitfit Ztirich 1982, Russian translation in: Kiberneticeskij Sbornik, Novaja Serija, Vyp. 22, Ed. 0,B. Lupanov, Mir Moscow (1985) 113- 158
    • Heintz, J. Definability and -fast quantifier elimination in algebraically closed fields (1983 (a)) Ph.-D. thesis, Universitfit Ztirich 1982. Theoret. Comput, Sci. 24 (1983) 239-277. Russian translation in: Kiberneticeskij Sbornik, Novaja Serija, Vyp. 22, Ed. 0,B. Lupanov, Mir Moscow (1985) 113- 158.
    • (1983) Theoret. Comput, Sci , vol.24 , pp. 239-277
    • Heintz, J.1
  • 24
    • 0022918062 scopus 로고
    • A Polynomials with Symmetric Galois Group which are Easy to Compute (1986)
    • Heintz, J. A Polynomials with Symmetric Galois Group which are Easy to Compute (1986) Theoret. Comput. Sci. 47 (1986) 99-105.
    • (1986) Theoret. Comput. Sci , vol.47 , pp. 99-105
    • Heintz, J.1
  • 26
    • 84944060784 scopus 로고
    • An international Symposium held in honour of Ernst Specker. Monographie No. 30 de L’Enseignement Math6matique, Geneve 1982, 237-254; also published in: 12th Annual Symposium ACM on Computing
    • Heintz, J. & Schnorr, C.P. Testing Polynomials which are Easy to Compute (1982) Logic and Algorithmic. An international Symposium held in honour of Ernst Specker. Monographie No. 30 de L’Enseignement Math6matique, Geneve 1982, 237-254; also published in: 12th Annual Symposium ACM on Computing (1980) 262-280.
    • (1980) Testing Polynomials Which are Easy to Compute (1982) Logic and Algorithmic , pp. 262-280
    • Heintz, J.1    Schnorr, C.P.2
  • 27
    • 0001638259 scopus 로고
    • Lower bounds for polynomials with algebraic coefficients (1980)
    • Heintz, J. & Sieveking M. Lower bounds for polynomials with algebraic coefficients (1980) Theoret. Comput. Sci. 11 (1980) 321-330.
    • (1980) Theoret. Comput. Sci , vol.11 , pp. 321-330
    • Heintz, J.1    Sieveking, M.2
  • 28
    • 0002694831 scopus 로고    scopus 로고
    • Absolute Primality of Polynomials is Decidable in Random Polynomial Time in the Number Of Variables (1981) 8th International Colloquium on Automata, Languages, and Programming ICALP 81
    • Heintz, J. & Sieveking M. Absolute Primality of Polynomials is Decidable in Random Polynomial Time in the Number Of Variables (1981) 8th International Colloquium on Automata, Languages, and Programming ICALP 81. LN Comput. Sci. 115, Springer Verlag, Berlin, 16-28.
    • LN Comput. Sci , vol.115 , pp. 16-28
    • Heintz, J.1    Sieveking, M.2
  • 31
    • 0004265088 scopus 로고
    • Interscience Publ. Wiley, New York
    • Lang, S. Diophantine Geometry (1962) Interscience Publ. Wiley, New York.
    • (1962) Diophantine Geometry
    • Lang, S.1
  • 33
    • 85034780626 scopus 로고
    • Die algorithmische Strulctur der sl(2,k) (1985) Master' s thesis, Universitat Frankfurt/M. An English abstract in: Proceedings of the AAECC-3 Conference, Grenoble 1985
    • Springer, Berlin Heidelberg
    • Mirwald, R. Die algorithmische Strulctur der sl(2,k) (1985) Master’s thesis, Universitat Frankfurt/M. an English abstract in: Proceedings of the AAECC-3 Conference, Grenoble 1985. LN Comput. Sci. 229, Springer, Berlin Heidelberg (1986) 274-287.
    • (1986) LN Comput. Sci , vol.229 , pp. 274-287
    • Mirwald, R.1
  • 35
    • 85034749684 scopus 로고
    • Preprint, University of Nice
    • Morgenstern, J. Preprint (1984), University of Nice.
    • (1984)
    • Morgenstern, J.1
  • 36
    • 0004473725 scopus 로고
    • Evaluation of polynomials and evaluation of rational functions (1955)
    • Motzkin, T.S. Evaluation of polynomials and evaluation of rational functions (1955) Bull. AMS 61 (1955) 163.
    • (1955) Bull. AMS , vol.61
    • Motzkin, T.S.1
  • 37
    • 0002705354 scopus 로고
    • On two problems in abstract algebre connected with Homer’s rule (1954)
    • presented to Richard von Mises, Academic Press, New York
    • Ostrowski, A.M. On two problems in abstract algebre connected with Homer’s rule (1954) Studies in Math. and Mech. presented to Richard von Mises, Academic Press, New York (1954) 40-44.
    • (1954) Studies in Math. And Mech , pp. 40-44
    • Ostrowski, A.M.1
  • 39
    • 0002534227 scopus 로고
    • On the number of nonscalar multiplications necessary to evaluate polynomials (1973)
    • Paterson, M.S. & Stockmeyer, L.J. On the number of nonscalar multiplications necessary to evaluate polynomials (1973) SIAM J. Comput. 2 (1973) 60-86.
    • (1973) SIAM J. Comput , vol.2 , pp. 60-86
    • Paterson, M.S.1    Stockmeyer, L.J.2
  • 40
    • 0022010891 scopus 로고
    • Additive complexity and zeros of real polynomials
    • 1985
    • Risler, J.J. Additive complexity and zeros of real polynomials (1985) SIAM J. Comput. 14 (1985) 178-183.
    • (1985) SIAM J. Comput. , vol.14 , pp. 178-183
    • Risler, J.J.1
  • 42
    • 0001205526 scopus 로고
    • Improved lower bounds on the number of multiplications,divisions which are necessary to evaluate polynomials
    • (1978
    • Schnorr, C.P. Improved lower bounds on the number of multiplications,divisions which are necessary to evaluate polynomials (1978) Theoret. Comput. Sci. 7 (1978) 251-261.
    • (1978) Theoret. Comput. Sci , vol.7 , pp. 251-261
    • Schnorr, C.P.1
  • 43
    • 0011668791 scopus 로고
    • An extension of Strassen’s degree bound
    • (1981)
    • Schnorr, C.P. An extension of Strassen’s degree bound (1981) SIAM J. Comput. 10 (1981) 371-382.
    • (1981) SIAM J. Comput , vol.10 , pp. 371-382
    • Schnorr, C.P.1
  • 44
    • 0011609133 scopus 로고
    • An elementary profsor Strassen ’s degree bound (1976)
    • Schönhage, A. An elementary profsor Strassen ’s degree bound (1976) Theoret. Comput. Sci. 3 (1976) 267-272.
    • (1976) Theoret. Comput. Sci , vol.3 , pp. 267-272
    • Schönhage, A.1
  • 45
    • 0013069009 scopus 로고
    • Partial and total matrix multiplication (1981)
    • Schönhage, A. Partial and total matrix multiplication (1981) SIAM J. Comput. 10 (1981) 434-455.
    • (1981) SIAM J. Comput , vol.10 , pp. 434-455
    • Schönhage, A.1
  • 47
    • 85034745864 scopus 로고    scopus 로고
    • Preprint, Universität Konstanz
    • Preprint, Universität Konstanz.
  • 49
    • 30244484542 scopus 로고
    • Evaluation of rational functions
    • R. Miller and J. Thatcher (Eds.), Plenum Press (1972)
    • Strassen, V. Evaluation of rational functions (1972) in: Complexity of Computer Computations, R. Miller and J. Thatcher (Eds.), Plenum Press (1972) 1- 10.
    • (1972) Complexity of Computer Computations
    • Strassen, V.1
  • 51
    • 0001063303 scopus 로고
    • Berechnungskomplexität von elementarsymmetrischen Funictionen und yon Interpolationskoeffizienten
    • 1973 (b)
    • Strassen, V. Berechnungskomplexität von elementarsymmetrischen Funictionen und yon Interpolationskoeffizienten (1973 (b)) Numer. Mathematik 20-3 (1973) 238- 251.
    • (1973) Numer. Mathematik , vol.20 , Issue.3
    • Strassen, V.1
  • 52
    • 0000155802 scopus 로고
    • Polynomials with rational coefficients which are hard to compute
    • (1974)
    • Strassen, V. Polynomials with rational coefficients which are hard to compute (1974) SIAM J. Comput. 3-2 (1974) 128-149.
    • (1974) SIAM J. Comput , vol.3 , Issue.2 , pp. 128-149
    • Strassen, V.1
  • 53
    • 0039916842 scopus 로고
    • Algebaische Berechnungskomplezität
    • Anniversary of Oberwolfach 1984, Birkhäiuser Verlag, Basel
    • Strassen, V. Algebaische Berechnungskomplezität (1984) in: Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Birkhäiuser Verlag, Basel, 509-550.
    • (1984) In: Perspectives in Mathematics , pp. 509-550
    • Strassen, V.1
  • 55
    • 0346498689 scopus 로고
    • Die Selterdzeit der Gleichungen mit Affekt
    • 1934
    • van der Waerden, B.L. Die Selterdzeit der Gleichungen mit Affekt (1934) Math. Annalen 109 (1934) 13-16.
    • (1934) Math. Annalen , vol.109 , pp. 13-16
    • Van Der Waerden, B.L.1
  • 57
    • 0017153710 scopus 로고
    • On computing the discrete Fourier transform
    • (1976)
    • Winograd, S, On computing the discrete Fourier transform (1976) Proc. Nat. Aead, Sci. USA 73 (1976) 1005-1006.
    • (1976) Proc. Nat. Aead, Sci. USA , vol.73 , pp. 1005-1006
    • Winograd, S.1
  • 58
    • 0004288395 scopus 로고
    • Some bilinear forms whose multiplicative complexity depends on the field of constants
    • 1977
    • Winograd, S. Some bilinear forms whose multiplicative complexity depends on the field of constants (1977) Math. Systems Theory 10 (1977) 169-180.
    • (1977) Math. Systems Theory , vol.10 , pp. 169-180
    • Winograd, S.1


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