메뉴 건너뛰기




Volumn 58, Issue 3, 1999, Pages 572-596

Computational complexity of some problems of linear algebra

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; LINEAR ALGEBRA; LINGUISTICS; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS;

EID: 0032679680     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1998.1608     Document Type: Article
Times cited : (117)

References (33)
  • 4
    • 0027806871 scopus 로고    scopus 로고
    • The complexity of the theory of p-adic numbers
    • "Proc. 34th Ann. Symp. Found. Comput. Sci., 1993," to appear
    • L. Egidi, The complexity of the theory of p-adic numbers, in "Proc. 34th Ann. Symp. Found. Comput. Sci., 1993," pp. 412-421, [Comput. Complexity, to appear].
    • Comput. Complexity , pp. 412-421
    • Egidi, L.1
  • 6
    • 0008631899 scopus 로고
    • A note on matrix rigidity
    • J. Friedman, A note on matrix rigidity, Combinatorica 13 (1993), 235-239.
    • (1993) Combinatorica , vol.13 , pp. 235-239
    • Friedman, J.1
  • 9
    • 0344493067 scopus 로고
    • Approximation de séries formelles par des séries rationnelles
    • C. Hespel, Approximation de séries formelles par des séries rationnelles, RAIRO Inform. Théor. 18 (1984), 241-258.
    • (1984) RAIRO Inform. Théor. , vol.18 , pp. 241-258
    • Hespel, C.1
  • 12
    • 0030497381 scopus 로고    scopus 로고
    • Hilbert's nullstellensatz is in the polynomial hierarchy
    • P. Koiran, Hilbert's nullstellensatz is in the polynomial hierarchy, J. Complexity 12 (1996), 273-286.
    • (1996) J. Complexity , vol.12 , pp. 273-286
    • Koiran, P.1
  • 13
    • 0003956970 scopus 로고
    • Addison-Wesley, Reading, MA
    • S. Lang, "Algebra," Addison-Wesley, Reading, MA, 1971.
    • (1971) Algebra
    • Lang, S.1
  • 14
    • 0029488086 scopus 로고
    • Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity
    • S. V. Lokam, Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity, in "Proc. 36th Ann. Symp. Found. Comput. Sci., 1995," pp. 6-16, 1995.
    • (1995) Proc. 36th Ann. Symp. Found. Comput. Sci., 1995 , pp. 6-16
    • Lokam, S.V.1
  • 16
    • 0026366408 scopus 로고
    • Optimization, approximation, and complexity classes
    • C. H. Papadimitriou and M. Yannakakis, Optimization, approximation, and complexity classes, J. Comput. System Sci. 43 (1991), 425-440.
    • (1991) J. Comput. System Sci. , vol.43 , pp. 425-440
    • Papadimitriou, C.H.1    Yannakakis, M.2
  • 17
    • 85025505234 scopus 로고
    • On the computational complexity and geometry of the first-order theory of the reals, part 1: Introduction, preliminaries. the geometry of semi-algebraic sets. the decision problem for the existential theory of the reals
    • J. Renegar, On the computational complexity and geometry of the first-order theory of the reals, part 1: Introduction, preliminaries. the geometry of semi-algebraic sets. the decision problem for the existential theory of the reals, J. Symbolic Comput. 13 (1992), 255-299.
    • (1992) J. Symbolic Comput. , vol.13 , pp. 255-299
    • Renegar, J.1
  • 18
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • J. T. Schwartz, Fast probabilistic algorithms for verification of polynomial identities, J. Assoc. Comput. Mach. 27 (1980), 701-717.
    • (1980) J. Assoc. Comput. Mach. , vol.27 , pp. 701-717
    • Schwartz, J.T.1
  • 20
    • 85016972944 scopus 로고
    • Graph-theoretic arguments in low-level complexity
    • "6th Mathematical Foundations of Computer Science, Springer-Verlag, New York/Berlin
    • L. Valiant, Graph-theoretic arguments in low-level complexity, in "6th Mathematical Foundations of Computer Science," Lecture Notes in Computer Science, Vol.197, pp. 162-176, Springer-Verlag, New York/Berlin, 1977.
    • (1977) Lecture Notes in Computer Science , vol.197 , pp. 162-176
    • Valiant, L.1
  • 22
    • 0001104119 scopus 로고
    • Ranks of completions of partial matrices
    • Calgary, AB
    • N. Cohen, C. R. Johnson, L. Rodman, and H. Woerdeman, Ranks of completions of partial matrices, The Gohberg anniversary collection, Vol.I (Calgary, AB, 1988), pp. 165-185, Oper. Theory: Adv. Appl., Vol. 40, Birkhäuser, Basel, 1989.
    • (1988) The Gohberg Anniversary Collection , vol.1 , pp. 165-185
    • Cohen, N.1    Johnson, C.R.2    Rodman, L.3    Woerdeman, H.4
  • 23
    • 85031627722 scopus 로고
    • Birkhäuser, Basel
    • N. Cohen, C. R. Johnson, L. Rodman, and H. Woerdeman, Ranks of completions of partial matrices, The Gohberg anniversary collection, Vol.I (Calgary, AB, 1988), pp. 165-185, Oper. Theory: Adv. Appl., Vol. 40, Birkhäuser, Basel, 1989.
    • (1989) Oper. Theory: Adv. Appl. , vol.40
  • 24
    • 84981753513 scopus 로고
    • Decision procedures for real and p-adic fields
    • P. J. Cohen, Decision procedures for real and p-adic fields, Comm. Pure Appl. Math. 22 (1969), 131-151.
    • (1969) Comm. Pure Appl. Math. , vol.22 , pp. 131-151
    • Cohen, P.J.1
  • 25
    • 0002167079 scopus 로고
    • Submodular functions, matroids and certain polyhedra
    • (R. Guy et al., Eds.), Gordon & Breach, New York
    • J. Edmonds, Submodular functions, matroids and certain polyhedra, in "Combinatorial Structures and Their Applications" (R. Guy et al., Eds.), pp. 69-87, Gordon & Breach, New York, 1970.
    • (1970) Combinatorial Structures and Their Applications , pp. 69-87
    • Edmonds, J.1
  • 26
    • 0001228489 scopus 로고
    • Systems of distinct representatives and linear algebra
    • J. Edmonds, Systems of distinct representatives and linear algebra, J. Res. Nat. Bur. Standards B 71 (1967), 241-245.
    • (1967) J. Res. Nat. Bur. Standards B , vol.71 , pp. 241-245
    • Edmonds, J.1
  • 27
    • 0032282618 scopus 로고    scopus 로고
    • A quantifier elimination for the theory of p-adic numbers
    • L. Egidi, A quantifier elimination for the theory of p-adic numbers, Comput. Complexity 7 (1998), 205-263.
    • (1998) Comput. Complexity , vol.7 , pp. 205-263
    • Egidi, L.1
  • 28
    • 0039627817 scopus 로고    scopus 로고
    • Maximum rank matrix completion
    • J. F. Geelen, Maximum rank matrix completion, Linear Algebra Appl. 288 (1999), 211-217.
    • (1999) Linear Algebra Appl. , vol.288 , pp. 211-217
    • Geelen, J.F.1
  • 29
    • 0038842848 scopus 로고
    • A determinantal version of the Frobenius-König theorem
    • D. J. Hartfiel and R. Loewy, A determinantal version of the Frobenius-König theorem, Linear Multilinear Algebra 16 (1984), 155-166.
    • (1984) Linear Multilinear Algebra , vol.16 , pp. 155-166
    • Hartfiel, D.J.1    Loewy, R.2
  • 30
    • 3042743084 scopus 로고    scopus 로고
    • Matrix completion problems
    • (C. A. Floudas and P. M. Pardalos, Eds.), Kluwer, Dordrecht, to appear
    • M. Laurent, Matrix completion problems, in "Encyclopedia of Optimization" (C. A. Floudas and P. M. Pardalos, Eds.), Kluwer, Dordrecht, to appear.
    • Encyclopedia of Optimization
    • Laurent, M.1
  • 31
    • 0003221566 scopus 로고
    • On determinants, matchings, and random algorithms
    • (L. Budach, Ed.), Akademie-Verlag, Berlin
    • L. Lovász, On determinants, matchings, and random algorithms, in "Fundamentals of Computation Theory, FCT '79" (L. Budach, Ed.), pp. 565-574, Akademie-Verlag, Berlin, 1979.
    • (1979) Fundamentals of Computation Theory, FCT '79 , pp. 565-574
    • Lovász, L.1
  • 32
    • 0009117949 scopus 로고
    • Mixed matrices: Irreducibility and decomposition
    • (R. A. Brunaldi, S. Friedland, and V. Klee, Eds.), Springer-Verlag, New York
    • K. Murota, Mixed matrices: Irreducibility and decomposition, in "Combinatorial and Graph-Theoretical Problems in Linear Algebra" (R. A. Brunaldi, S. Friedland, and V. Klee, Eds.), pp. 39-71, Springer-Verlag, New York, 1993.
    • (1993) Combinatorial and Graph-Theoretical Problems in Linear Algebra , pp. 39-71
    • Murota, K.1
  • 33
    • 0346065708 scopus 로고
    • Matrix and Operator Extensions
    • Centrum voor Wiskunde en Informatica, Amsterdam
    • H. J. Woerdeman, "Matrix and Operator Extensions," CWI Tract 68, Centrum voor Wiskunde en Informatica, Amsterdam, 1989.
    • (1989) CWI Tract 68
    • Woerdeman, H.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.