메뉴 건너뛰기




Volumn 8, Issue 5, 2008, Pages 607-647

Semidefinite characterization and computation of zero-dimensional real radical ideals

Author keywords

(Real) radical ideal; Algebraic geometry; Semidefinite programming; Zero dimensional ideal

Indexed keywords

(REAL) RADICAL IDEAL; ALGEBRAIC GEOMETRY; COMPLEX COMPONENTS; NUMERICAL LINEAR ALGEBRA; SEMI-DEFINITE PROGRAMMING; SEMIDEFINITE OPTIMIZATION; ZERO-DIMENSIONAL; ZERO-DIMENSIONAL IDEAL;

EID: 52949150070     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-007-9004-y     Document Type: Article
Times cited : (93)

References (45)
  • 1
    • 0002083724 scopus 로고
    • Computation of real radicals of polynomial ideals
    • Progress in Mathematics Birkhäuser Boston
    • E. Becker and R. Neuhaus, Computation of real radicals of polynomial ideals, in Computational Algebraic Geometry (F. Eyssette and A. Galligo, eds.), Progress in Mathematics, Vol. 109, pp. 1-20, Birkhäuser, Boston, 1993.
    • (1993) Computational Algebraic Geometry , vol.109 , pp. 1-20
    • Becker, E.1    Neuhaus, R.2    Eyssette, F.3    Galligo, A.4
  • 3
    • 0030285763 scopus 로고    scopus 로고
    • Radical computations of zero-dimensional ideals and real root counting
    • E. Becker T. Wörmann 1996 Radical computations of zero-dimensional ideals and real root counting Math. Comput. Simul. 42 561 569
    • (1996) Math. Comput. Simul. , vol.42 , pp. 561-569
    • Becker, E.1    Wörmann, T.2
  • 5
    • 47649108476 scopus 로고    scopus 로고
    • New fewnomial upper bounds from Gale dual polynomial systems
    • F. Bihan and F. Sottile, New fewnomial upper bounds from Gale dual polynomial systems, Moscow Math. J., 7(3) (2007).
    • (2007) Moscow Math. J. , vol.7 , Issue.3
    • Bihan, F.1    Sottile, F.2
  • 12
    • 0029684826 scopus 로고    scopus 로고
    • Solution of the truncated complex moment problem for flat data
    • R. Curto and L. Fialkow, Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc. 119(568) (1996).
    • (1996) Mem. Amer. Math. Soc. , vol.119 , Issue.568
    • Curto, R.1    Fialkow, L.2
  • 13
    • 23044517911 scopus 로고    scopus 로고
    • The truncated complex K-moment problem
    • R. Curto L. Fialkow 2000 The truncated complex K-moment problem Trans. Amer. Math. Soc. 352 2825 2855
    • (2000) Trans. Amer. Math. Soc. , vol.352 , pp. 2825-2855
    • Curto, R.1    Fialkow, L.2
  • 14
    • 0036763607 scopus 로고    scopus 로고
    • Solution of the singular quartic moment problem
    • R. Curto L. Fialkow 2002 Solution of the singular quartic moment problem J. Oper. Theory 48 315 354
    • (2002) J. Oper. Theory , vol.48 , pp. 315-354
    • Curto, R.1    Fialkow, L.2
  • 19
    • 85025504292 scopus 로고
    • Gröbner bases and primary decomposition of polynomial ideals
    • P. Gianni B. Trager G. Zacharias 1988 Gröbner bases and primary decomposition of polynomial ideals J. Symb. Comput. 6 149 167
    • (1988) J. Symb. Comput. , vol.6 , pp. 149-167
    • Gianni, P.1    Trager, B.2    Zacharias, G.3
  • 20
    • 0032332553 scopus 로고    scopus 로고
    • Interior point trajectories in semidefinite programming
    • D. Goldfarb K. Scheinberg 1998 Interior point trajectories in semidefinite programming SIAM J. Optim. 8 871 886
    • (1998) SIAM J. Optim. , vol.8 , pp. 871-886
    • Goldfarb, D.1    Scheinberg, K.2
  • 21
    • 33947537644 scopus 로고    scopus 로고
    • Detecting global optimality and extracting solutions in gloptiPoly
    • Lectures Notes in Control and Information Sciences Springer New York
    • D. Henrion and J. B. Lasserre, Detecting global optimality and extracting solutions in gloptiPoly, in Positive Polynomials in Control (D. Henrion and A. Garulli, eds.), Lectures Notes in Control and Information Sciences, Vol. 312, pp. 293-310, Springer, New York, 2005.
    • (2005) Positive Polynomials in Control , vol.312 , pp. 293-310
    • Henrion, D.1    Lasserre, J.B.2    Henrion, D.3    Garulli, A.4
  • 22
    • 0004015202 scopus 로고
    • Am. Math. Soc. Providence
    • A. G. Khovanski, Fewnomials, Am. Math. Soc., Providence, 1991.
    • (1991) Fewnomials
    • Khovanski, A.G.1
  • 23
    • 85030645974 scopus 로고
    • An algorithm for the computation of the radical of an ideal in the ring of polynomials
    • New Orleans, LA, 1991, Lecture Notes in Computer Science Springer, Berlin
    • T. Krick and A. Logar, An algorithm for the computation of the radical of an ideal in the ring of polynomials, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (New Orleans, LA, 1991), Lecture Notes in Computer Science, Vol. 539, pp. 195-205, Springer, Berlin, 1991.
    • (1991) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes , vol.539 , pp. 195-205
    • Krick, T.1    Logar, A.2
  • 24
    • 0003367986 scopus 로고
    • On the complexity of zero-dimensional algebraic systems
    • T. Mora and C. Traverso, eds., Progress in Mathematics Birkhäuser, Boston
    • Y. N. Lakshman and D. Lazard, On the complexity of zero-dimensional algebraic systems, in Effective Methods in Algebraic Geometry (T. Mora and C. Traverso, eds.), Progress in Mathematics, Vol. 94, pp. 217-226, Birkhäuser, Boston, 1991.
    • (1991) Effective Methods in Algebraic Geometry , vol.94 , pp. 217-226
    • Lakshman, Y.N.1    Lazard, D.2
  • 25
    • 0035238864 scopus 로고    scopus 로고
    • Global optimization with polynomials and the problem of moments
    • J. B. Lasserre 2001 Global optimization with polynomials and the problem of moments SIAM J. Optim. 11 796 817
    • (2001) SIAM J. Optim. , vol.11 , pp. 796-817
    • Lasserre, J.B.1
  • 26
    • 33645756017 scopus 로고    scopus 로고
    • A moment approach to analyze zeros of triangular polynomial sets
    • J. B. Lasserre 2006 A moment approach to analyze zeros of triangular polynomial sets Trans. Amer. Math. Soc. 358 1403 1420
    • (2006) Trans. Amer. Math. Soc. , vol.358 , pp. 1403-1420
    • Lasserre, J.B.1
  • 27
    • 26444549416 scopus 로고    scopus 로고
    • Revisiting two theorems of Curto and Fialkow
    • 10
    • M. Laurent 2005 Revisiting two theorems of Curto and Fialkow Proc. Amer. Math. Soc. 133 10 2965 2976
    • (2005) Proc. Amer. Math. Soc. , vol.133 , pp. 2965-2976
    • Laurent, M.1
  • 28
    • 33845284255 scopus 로고    scopus 로고
    • Semidefinite representations for finite varieties
    • M. Laurent 2007 Semidefinite representations for finite varieties Math. Program. 109 1 26
    • (2007) Math. Program. , vol.109 , pp. 1-26
    • Laurent, M.1
  • 30
    • 20344396845 scopus 로고    scopus 로고
    • YALMIP: A toolbox for modeling and optimization in MATLAB
    • Taipei, Taiwan
    • J. Löfberg, YALMIP: A toolbox for modeling and optimization in MATLAB, in Proceedings of CACSD, Taipei, Taiwan, 2004. Available from http://control.ee.ethz.ch/~joloef/yalmip.php.
    • (2004) Proceedings of CACSD
    • Löfberg, J.1
  • 31
    • 0003058684 scopus 로고    scopus 로고
    • A new criterion for normal form algorithms
    • M. Fossorier et al., eds., Lecture Notes in Computer Science Springer Berlin
    • B. Mourrain, A new criterion for normal form algorithms, in Proc. Conf. AAECC-13, Honolulu, 1999 (M. Fossorier et al., eds.), Lecture Notes in Computer Science, Vol. 1719, pp. 431-443, Springer, Berlin, 1999.
    • (1999) Proc. Conf. AAECC-13, Honolulu, 1999 , vol.1719 , pp. 431-443
    • Mourrain, B.1
  • 32
    • 0000413093 scopus 로고
    • Counting real zeros in the multivariate case
    • F. Eyssette, A. Galligo, eds., Progress in Mathematics, Birkhäuser Boston
    • P. Pedersen, M.-F. Roy, and A. Szpirglas, Counting real zeros in the multivariate case, in Computational Algebraic Geometry (F. Eyssette, A. Galligo, eds.), Progress in Mathematics, Vol. 109, pp. 203-224, Birkhäuser, Boston, 1993.
    • (1993) Computational Algebraic Geometry , vol.109 , pp. 203-224
    • Pedersen, P.1    Roy, M.-F.2    Szpirglas, A.3
  • 34
    • 22344435283 scopus 로고    scopus 로고
    • Motivations for an arbitrary precision interval arithmetic and the MPFI library
    • N. Revol F. Rouillier 2005 Motivations for an arbitrary precision interval arithmetic and the MPFI library Reliable Comput. 11 1 16
    • (2005) Reliable Comput. , vol.11 , pp. 1-16
    • Revol, N.1    Rouillier, F.2
  • 35
    • 0033131339 scopus 로고    scopus 로고
    • Solving zero-dimensional systems through the rational univariate representation
    • F. Rouillier 1999 Solving zero-dimensional systems through the rational univariate representation J. Appl. Algebra Eng. Commun. Comput. 9 433 461
    • (1999) J. Appl. Algebra Eng. Commun. Comput. , vol.9 , pp. 433-461
    • Rouillier, F.1
  • 38
    • 34250416099 scopus 로고
    • A Nullstellensatz and a Positivstellensatz in semialgebraic geometry
    • G. Stengle 1974 A Nullstellensatz and a Positivstellensatz in semialgebraic geometry Math. Ann. 207 87 97
    • (1974) Math. Ann. , vol.207 , pp. 87-97
    • Stengle, G.1
  • 40
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • Special issue on Interior Point Methods (CD supplement with software)
    • J. F. Sturm 1999 Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones Optim. Methods Softw. 11/12 625 653 Special issue on Interior Point Methods (CD supplement with software)
    • (1999) Optim. Methods Softw. , vol.1112 , pp. 625-653
    • Sturm, J.F.1
  • 41
    • 0036923521 scopus 로고    scopus 로고
    • Implementation of interior point methods for mixed semidefinite and second order cone optimization problems
    • 6
    • J. F. Sturm 2002 Implementation of interior point methods for mixed semidefinite and second order cone optimization problems Optim. Methods Softw. 17 6 1105 1154
    • (2002) Optim. Methods Softw. , vol.17 , pp. 1105-1154
    • Sturm, J.F.1
  • 42
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • 1
    • L. Vandenberghe S. Boyd 1996 Semidefinite programming SIAM Rev. 38 1 49 95
    • (1996) SIAM Rev. , vol.38 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 43
    • 0001656792 scopus 로고    scopus 로고
    • Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation
    • 2
    • J. Verschelde 1999 Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation ACM Trans. Math. Softw. 25 2 251 276
    • (1999) ACM Trans. Math. Softw. , vol.25 , pp. 251-276
    • Verschelde, J.1
  • 44
    • 0001917438 scopus 로고
    • Symmetric Newton polytopes for solving sparse polynomial systems
    • 1
    • J. Verschelde K. Gatermann 1995 Symmetric Newton polytopes for solving sparse polynomial systems Adv. Appl. Math. 16 1 95 127
    • (1995) Adv. Appl. Math. , vol.16 , pp. 95-127
    • Verschelde, J.1    Gatermann, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.