À propos de cet article

Citez

[1] E. L. Allgower and K. Georg. Numerical Continuation Methods, an Introduction, Springer Series in Comput. Math, Vol. 13, Springer-Veralg, Berlin, Heidelberg, New Yourk, 1990.10.1007/978-3-642-61257-2Search in Google Scholar

[2] E. Arbarello, M. Coranalba, P.A. Griffths and J. Harris. Geometry of Algebraic Curves, volume I. Volume 267 of Grundlehren Math. Wiss., Springer Verlag, New York, 1985.Search in Google Scholar

[3] D. J. Bates, J. D. Hauenstein, A. J. Sommese and C. W. Wampler. Bertini : Software for Numerical Algebraic Geometry. http://www.nd.edu/~sommese/bertini/.Search in Google Scholar

[4] S. C. Billups, A. P. Morgan and L. T. Watson. Algorithm 652. Hompack: A Suite codes for Globally Convergent Homotopy Algorithms. ACM Transactions on Mathematical Software, Vol.13. No. 3, Septemper 1987, Pages 281-310.10.1145/29380.214343Search in Google Scholar

[5] G. Björck and R. Fröberg. A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots. J. Symbolic Computation, 12:329-336, 1991.10.1016/S0747-7171(08)80153-8Search in Google Scholar

[6] G. Björck. Functions of modulus one on Zn whose Fourier transforms have constant modulus, and cyclic n-roots. In: J. S. Byrnes and J. F. Byrnes, Editors, Recent Advances in Fourier Analysis and its Applications 315, NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., Kluwer (1989), pp. 131-140.10.1007/978-94-009-0665-5_10Search in Google Scholar

[7] R. M. Corless, A. Galligo, I. S. Kotsireas and S. M. Watt. A Geometric-Numeric Algorithm for Absolute Factorization of Multivariate Polynomials. ISSAC 2002, July 7-10, 2002, Lille, France.10.1145/780506.780512Search in Google Scholar

[8] W. Decker, G.-M. Greuel, G. Pfister and H. Schönemann. Singular 3-1-1 — A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2010).Search in Google Scholar

[9] G. Fischer. Complex Alalytic Geometry, Lecture Notes in Mathematics 538 (1976).10.1007/BFb0080338Search in Google Scholar

[10] W. Fulton. Intersection Theory, volume (3) 2 of Ergeb. Math. Grenzgeb. Springer Verlag, Berlin, 1984.10.1007/978-3-662-02421-8_18Search in Google Scholar

[11] G.-M. Greuel and G. Pfister. A SingularIntroduction to Commutative Algebra. Second edition, Springer (2007).Search in Google Scholar

[12] A. P. Morgan and L. T. Watson. A globally convergent parallel algorithm for zeros of polynomial systems. Nonlinear Anal. (1989), 13(11), 1339–1350.10.1016/0362-546X(89)90017-5Search in Google Scholar

[13] A. P. Morgan and A. J. Sommese. Computing all solutions to polynomial systems using homotopy continuation. Appl. Math. Comput., 115-138. Errata: Appl. Math. Comput. 51 (1992), p. 209. Nonlinear Anal.10.1016/0096-3003(92)90075-CSearch in Google Scholar

[14] A. J. Sommese, J. Verschelde and C. W. Wampler. Symmetric functions applied to decomposing solution sets of polynomial systems. Vol. 40, No. 6, pp. 2026-2046. 2002 Society for Industrial and Applied Mathematics.10.1137/S0036142901397101Search in Google Scholar

[15] A. J. Sommese and J. Verschelde. Numerical homotopies to compute generic points on positive dimensional algebraic sets. J. of Complexity 16(3):572-602, (2000).10.1006/jcom.2000.0554Search in Google Scholar

[16] A. J. Sommese, C. W. Wampler and J. D. Hauenstein. Regenerative cascade homotopies for solving polynomial systems. Applied Mathematics and Computation 218(4): 1240-1246 (2011)10.1016/j.amc.2011.06.004Search in Google Scholar

[17] A. J. Sommese, J. Verschelde and C. W. Wampler. (2002a). A method for tracking singular paths with application to the numerical decomposition. In algebraic geometry (pp. 329-345). Berlin: de Gruyter.10.1515/9783110198072.329Search in Google Scholar

[18] A. J. Sommese, J. Verschelde and C. W. Wampler. (2001a). Numerical decomposition of solution sets of polynomial systems into irreducible components. SIAM J. Number. Anal., 38(6), 2022-2046. NID10.1137/S0036142900372549Search in Google Scholar

[19] A. J. Sommese, J. Verschelde and C. W. Wampler. (2003). Numerical irreducible decomposition using PHCpack. In algebra, geometry, and software systems (pp. 109-129). Berlin: Springer.Search in Google Scholar

[20] A. J. Sommese, J. Verschelde and C.W. Wampler. Numerical decomposition of the solution sets of polynomial systems into irreducible components. SIAM J. Numer. Anal. 38(6):2022-2046, 2001.10.1137/S0036142900372549Search in Google Scholar

[21] A. J. Sommese, J. Verschelde and C. W. Wampler. Numerical irreducible decomposition using projections from points on components. In Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering, volume 286 of contemporary Mathematics, edited by E. L. Green, S. Hosten, R. C. Laubenbacher and V. Powers, pages 27-51. AMS 2001.10.1090/conm/286/04753Search in Google Scholar

[22] A. J. Sommese, J. Verschelde and C. W. Wampler. Using monodromy to decompose solution sets of polynomial systems into irreducible components. In Application of Algebraic Geometry to Coding Theory, Physics and Computation, edited by C. Ciliberto, F. Hirzebruch, R. Miranda and M. Teicher. Proceedings of a NATO Conference, February 25-March 1, 2001, Eilat, Israel. Pages 297-315, Kluwer Academic Publishers.10.1007/978-94-010-1011-5_16Search in Google Scholar

[23] A. J. Sommese and C. W. Wampler. The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. ISBN 981-256-184-6. Word Scientific Publishing Co. Plte. Ltd. 2005.10.1142/5763Search in Google Scholar

[24] A. J. Sommese and C. W. Wampler. Numerical algebraic geometry. In the mathematics of numerical analysis. (Park City, UT, 1995), Vol. 32 of lectures in Appl. Math. (pp. 749-763). Providence, RI: Amer. Math. Soc.Search in Google Scholar

[25] J. Verschelde(1996). Homotopy continuation methods for solving polynomial systems. PhD thesis, Katholihe Universiteit Leuven.Search in Google Scholar

[26] J. Verschelde(1999). Algorithm 795: PHCpack:Ageneral-purpose solver for polynomial systems by homotopy continuation. ACM Trans. on Math. Software, 25(2), 251-276.10.1145/317275.317286Search in Google Scholar

eISSN:
1844-0835
Langue:
Anglais
Périodicité:
Volume Open
Sujets de la revue:
Mathematics, General Mathematics