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Volumn 218, Issue 4, 2011, Pages 1240-1246

Regenerative cascade homotopies for solving polynomial systems

Author keywords

Algebraic set; Cascade homotopy; Generic points; Homotopy continuation; Numerical algebraic geometry; Numerical irreducible decomposition; Polynomial system; Witness superset

Indexed keywords

ALGEBRAIC SET; GENERIC POINTS; HOMOTOPY CONTINUATION; IRREDUCIBLE DECOMPOSITION; NUMERICAL ALGEBRAIC GEOMETRY; POLYNOMIAL SYSTEM; WITNESS SUPERSET;

EID: 80052269897     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2011.06.004     Document Type: Article
Times cited : (34)

References (21)
  • 7
    • 78649385909 scopus 로고    scopus 로고
    • Regeneration homotopies for solving systems of polynomials
    • J.D. Hauenstein, A.J. Sommese, and C.W. Wampler Regeneration homotopies for solving systems of polynomials Math. Comput. 80 2011 345 377
    • (2011) Math. Comput. , vol.80 , pp. 345-377
    • Hauenstein, J.D.1    Sommese, A.J.2    Wampler, C.W.3
  • 8
    • 84968520678 scopus 로고
    • A polyhedral method for solving sparse polynomial systems
    • B. Huber, and B. Sturmfels A polyhedral method for solving sparse polynomial systems Math. Comput. 64 1995 1541 1555
    • (1995) Math. Comput. , vol.64 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 11
    • 77950341364 scopus 로고    scopus 로고
    • Higher-order deflation for polynomial systems with isolated singular solutions
    • A. Dickenstein, F.-O. Schreyer, A.J. Sommese, Algorithms in Algebraic Geometry Springer
    • A. Leykin, J. Verschelde, and A. Zhao Higher-order deflation for polynomial systems with isolated singular solutions A. Dickenstein, F.-O. Schreyer, A.J. Sommese, IMA Algorithms in Algebraic Geometry vol. 146 2008 Springer 79 97
    • (2008) IMA , vol.146 , pp. 79-97
    • Leykin, A.1    Verschelde, J.2    Zhao, A.3
  • 12
    • 33746348355 scopus 로고    scopus 로고
    • Newton's method with deflation for isolated singularities of polynomial systems
    • DOI 10.1016/j.tcs.2006.02.018, PII S030439750600168X
    • A. Leykin, J. Verschelde, and A. Zhao Newton's method with deflation for isolated singularities of polynomial systems Theor. Comput. Sci. 359 2006 111 122 (Pubitemid 44119067)
    • (2006) Theoretical Computer Science , vol.359 , Issue.1-3 , pp. 111-122
    • Leykin, A.1    Verschelde, J.2    Zhao, A.3
  • 13
    • 67649659716 scopus 로고    scopus 로고
    • Numerical solution of polynomial system by homotopy continuation methods
    • North-Holland Amsterdam
    • T.Y. Li Numerical solution of polynomial system by homotopy continuation methods Handbook of Numerical Analysis vol. XI 2003 North-Holland Amsterdam 209 304
    • (2003) Handbook of Numerical Analysis , vol.11 , pp. 209-304
    • Li, T.Y.1
  • 14
    • 0023329339 scopus 로고
    • Modified deflation algorithm for the solution of singular problems. I.A system of nonlinear algebraic equations
    • T. Ojika Modified deflation algorithm for the solution of singular problems. I.A system of nonlinear algebraic equations J. Math. Anal. Appl. 123 1987 199 221 (Pubitemid 17552208)
    • (1987) Journal of Mathematical Analysis and Applications , vol.123 , Issue.1 , pp. 199-221
    • Ojika Takeo1
  • 16
    • 0000158786 scopus 로고    scopus 로고
    • Numerical homotopies to compute generic points on positive dimensional algebraic sets
    • A.J. Sommese, and J. Verschelde Numerical homotopies to compute generic points on positive dimensional algebraic sets J. Complex. 16 2000 572 602
    • (2000) J. Complex. , vol.16 , pp. 572-602
    • Sommese, A.J.1    Verschelde, J.2
  • 17
    • 21844480967 scopus 로고    scopus 로고
    • Homotopies for intersecting solution components of polynomial systems
    • DOI 10.1137/S0036142903430463
    • A.J. Sommese, J. Verschelde, and C.W. Wampler Homotopies for intersecting solution components of polynomial systems SIAM J. Numer. Anal. 42 2004 1552 1571 (Pubitemid 41366164)
    • (2004) SIAM Journal on Numerical Analysis , vol.42 , Issue.4 , pp. 1552-1571
    • Sommese, A.J.1    Verschelde, J.2    Wampler, C.W.3
  • 18
    • 0010177750 scopus 로고    scopus 로고
    • Numerical algebraic geometry
    • J. Renegar, M. Shub, S. Smale (Eds.) Proceedings of the AMS-SIAM Summer Seminar in Applied Mathematics, Park City, Utah, July 17-August 11, 1995, Park City, Utah
    • A.J. Sommese, C.W. Wampler, Numerical algebraic geometry, in: J. Renegar, M. Shub, S. Smale (Eds.), The Mathematics of Numerical Analysis, Lectures in Applied Mathematics, vol. 32, 1996, pp. 749-763, Proceedings of the AMS-SIAM Summer Seminar in Applied Mathematics, Park City, Utah, July 17-August 11, 1995, Park City, Utah.
    • (1996) The Mathematics of Numerical Analysis, Lectures in Applied Mathematics , vol.32 , pp. 749-763
    • Sommese, A.J.1    Wampler, C.W.2
  • 20
    • 33746454263 scopus 로고    scopus 로고
    • Algorithm 857: POLSYS-GLP: A parallel general linear product homotopy code for solving polynomial systems of equations
    • H.-J. Su, J.M. McCarthy, M. Sosonkina, and L.T. Watson Algorithm 857: POLSYS-GLP: a parallel general linear product homotopy code for solving polynomial systems of equations ACM Trans. Math. Softw. 32 4 2006 561 579
    • (2006) ACM Trans. Math. Softw. , vol.32 , Issue.4 , pp. 561-579
    • Su, H.-J.1    McCarthy, J.M.2    Sosonkina, M.3    Watson, L.T.4
  • 21
    • 0001656792 scopus 로고    scopus 로고
    • Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation
    • J. Verschelde Algorithm 795: PHC pack: a general-purpose solver for polynomial systems by homotopy continuation ACM Trans. Math. Softw. 25 2 1999 251 276 (Pubitemid 129533740)
    • (1999) ACM Transactions on Mathematical Software , vol.25 , Issue.2 , pp. 251-276
    • Verschelde, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.