메뉴 건너뛰기




Volumn 73, Issue 1, 2004, Pages 57-77

PHoM - A polyhedral homotopy continuation method for polynomial systems

Author keywords

Equation; Homotopy continuation method; Numerical experiment; Polyhedral homotopy; Polynomial; Software package

Indexed keywords

COMPUTER SIMULATION; COMPUTER SOFTWARE; CONTROL NONLINEARITIES; DATA RECORDING; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL ANALYSIS;

EID: 4243094969     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-003-0032-4     Document Type: Article
Times cited : (45)

References (31)
  • 2
    • 0039067387 scopus 로고
    • Granularity issues for solving polynomial systems via globally convergent algorithms on a hypercube
    • Allison, D. C. S., Chakaborty, A., Watson, L. T.: Granularity issues for solving polynomial systems via globally convergent algorithms on a hypercube. J. Supercomputing 3, 5-20 (1989).
    • (1989) J. Supercomputing , vol.3 , pp. 5-20
    • Allison, D.C.S.1    Chakaborty, A.2    Watson, L.T.3
  • 4
    • 34250406508 scopus 로고
    • The number of roots of a system of equations
    • Bernshtein, D. N.: The number of roots of a system of equations. Funct. Anal. Appl. 9, 183-185 (1975).
    • (1975) Funct. Anal. Appl. , vol.9 , pp. 183-185
    • Bernshtein, D.N.1
  • 5
    • 0002820505 scopus 로고
    • Some examples for solving systems of algebraic equations by calculating Groebner bases
    • Boege, W., Gebauer, R., Kredel, H.: Some examples for solving systems of algebraic equations by calculating Groebner bases. J. Symbolic Comput. 2, 83-98 (1986).
    • (1986) J. Symbolic Comput. , vol.2 , pp. 83-98
    • Boege, W.1    Gebauer, R.2    Kredel, H.3
  • 6
    • 26344444273 scopus 로고
    • A faster way to count the solutions of unhomogeneous systems of algebraic equations, with applications to cyclic n-roots
    • Björck, G., Fröberg, R.: A faster way to count the solutions of unhomogeneous systems of algebraic equations, with applications to cyclic n-roots. J. Symbolic Comput. 12, 329-336 (1991).
    • (1991) J. Symbolic Comput. , vol.12 , pp. 329-336
    • Björck, G.1    Fröberg, R.2
  • 7
    • 0037334665 scopus 로고    scopus 로고
    • Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods
    • Dai, Y., Kim, S., Kojima, M.: Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods. J. Comput. Appl. Math. 152, 83-97 (2003).
    • (2003) J. Comput. Appl. Math. , vol.152 , pp. 83-97
    • Dai, Y.1    Kim, S.2    Kojima, M.3
  • 8
    • 0002403273 scopus 로고
    • Eine Methode zur Berechnung sämtlicher Lösungen von Polynomgleichungs-systemen
    • Drexler, F. J.: Eine Methode zur Berechnung sämtlicher Lösungen von Polynomgleichungs-systemen. Numer. Math. 29, 45-58 (1977).
    • (1977) Numer. Math. , vol.29 , pp. 45-58
    • Drexler, F.J.1
  • 10
    • 0018429579 scopus 로고
    • Determining all solutions to certain systems of nonlinear equations
    • Garcia, C. B., Zangwill, W. I.: Determining all solutions to certain systems of nonlinear equations. Math. Operations Res. 4, 1-14 (1979).
    • (1979) Math. Operations Res. , vol.4 , pp. 1-14
    • Garcia, C.B.1    Zangwill, W.I.2
  • 11
    • 0001731339 scopus 로고    scopus 로고
    • Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods
    • Gao, T., Li, T. Y., Verschelde, J., Wu, M.: Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods. Appl. Math. Comput. 114, 233-247 (2000).
    • (2000) Appl. Math. Comput. , vol.114 , pp. 233-247
    • Gao, T.1    Li, T.Y.2    Verschelde, J.3    Wu, M.4
  • 12
    • 84968520678 scopus 로고
    • A polyhedral method for solving sparse polynomial systems
    • Huber, B., Sturmfels, B.: A polyhedral method for solving sparse polynomial systems. Math. Comput. 64, 1541-1555 (1995).
    • (1995) Math. Comput. , vol.64 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 13
    • 0032355157 scopus 로고    scopus 로고
    • Polyhedral end games for polynomial continuation
    • Huber, B., Verschelde, J.: Polyhedral end games for polynomial continuation. Numer. Algorithms 18, 91-108 (1998).
    • (1998) Numer. Algorithms , vol.18 , pp. 91-108
    • Huber, B.1    Verschelde, J.2
  • 16
    • 84862399732 scopus 로고    scopus 로고
    • Kojima, M.: his web site: http://www.is.titech.ac.jp/~kojima/polynomials/ .
    • Kojima, M.1
  • 18
    • 0001444287 scopus 로고
    • The Cheater's homotopy: An efficient procedure for solving systems of polynomial equations
    • Li, T. Y., Sauer, T., York, J. A.: The Cheater's homotopy: an efficient procedure for solving systems of polynomial equations. SIAM J. Numer. Anal. 26, 1241-1251 (1989).
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 1241-1251
    • Li, T.Y.1    Sauer, T.2    York, J.A.3
  • 19
    • 0012328027 scopus 로고    scopus 로고
    • Solving polynomial systems by polyhedral homotopies
    • Li, T. Y.: Solving polynomial systems by polyhedral homotopies. Taiwan J. Math. 3, 251-279 (1999).
    • (1999) Taiwan J. Math. , vol.3 , pp. 251-279
    • Li, T.Y.1
  • 20
    • 0012316556 scopus 로고    scopus 로고
    • Finding mixed cells in the mixed volume computation
    • Li, T. Y., Li, X.: Finding mixed cells in the mixed volume computation. Foundation Comput. Math. 1, 161-181 (2001).
    • (2001) Foundation Comput. Math. , vol.1 , pp. 161-181
    • Li, T.Y.1    Li, X.2
  • 22
    • 0000749801 scopus 로고
    • Coefficient-parameter polynomial continuation
    • Morgan, A. P., Sommese, A. J.: Coefficient-parameter polynomial continuation. Appl. Math. Comput. 29, 123-160 (1989).
    • (1989) Appl. Math. Comput. , vol.29 , pp. 123-160
    • Morgan, A.P.1    Sommese, A.J.2
  • 23
    • 0000974924 scopus 로고
    • A neural network modeled by an adaptive Lotka-Volterra system
    • Noonberg, V. W.: A neural network modeled by an adaptive Lotka-Volterra system. SIAM J. Appl. Math. 49, 1779-1792 (1989).
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1779-1792
    • Noonberg, V.W.1
  • 25
    • 0242530938 scopus 로고    scopus 로고
    • Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method
    • Takeda, A., Kojima, M., Fujisawa, K.: Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method. J. Operations Soc. Japan 45, 64-82 (2002).
    • (2002) J. Operations Soc. Japan , vol.45 , pp. 64-82
    • Takeda, A.1    Kojima, M.2    Fujisawa, K.3
  • 28
    • 0028449799 scopus 로고
    • Homotopies exploiting Newton polytopes for solving sparse polynomial systems
    • Verschelde, J., Verlinden, P., Cools, R.: Homotopies exploiting Newton polytopes for solving sparse polynomial systems. SIAM J. Numer. Anal. 31, 915-930 (1994).
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 915-930
    • Verschelde, J.1    Verlinden, P.2    Cools, R.3
  • 29
    • 0001656792 scopus 로고    scopus 로고
    • Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation
    • Verschelde, J.: Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Softw. 25, 251-276 (1999).
    • (1999) ACM Trans. Math. Softw. , vol.25 , pp. 251-276
    • Verschelde, J.1
  • 30
    • 0023415939 scopus 로고
    • Algorithm 652: HOMPACK: A suite for codes for globally convergent homotopy algorithms
    • Watson, L. T., Billips, S. C., Morgan, A. P.: Algorithm 652: HOMPACK: a suite for codes for globally convergent homotopy algorithms. ACM Trans. Math. Softw. 13, 281-310 (1987).
    • (1987) ACM Trans. Math. Softw. , vol.13 , pp. 281-310
    • Watson, L.T.1    Billips, S.C.2    Morgan, A.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.