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Volumn 21, Issue 1, 2012, Pages 69-83

Certified numerical homotopy tracking

Author keywords

Approximate zero; Certified algorithms; Complexity; Computational aspects of algebraic geometry; Continual methods; Homotopy methods; Systems of equations

Indexed keywords


EID: 84866517015     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2011.606184     Document Type: Article
Times cited : (34)

References (28)
  • 2
    • 78650777725 scopus 로고    scopus 로고
    • A Continuation Method to Solve Polynomial Systems, and Its Complexity
    • C. Beltrán. "A Continuation Method to Solve Polynomial Systems, and Its Complexity." Numerische Mathematik 117:1 (2011), 89-113.
    • (2011) Numerische Mathematik , vol.117 , Issue.1 , pp. 89-113
    • Beltrán, C.1
  • 4
    • 44249086976 scopus 로고    scopus 로고
    • On Smale's 17th Problem: A Probabilistic Positive Solution
    • C. Beltrán and L. M. Pardo. "On Smale's 17th Problem: A Probabilistic Positive Solution." Found. Comput. Math. 8:1 (2008), 1-43.
    • (2008) Found. Comput. Math. , vol.8 , Issue.1 , pp. 1-43
    • Beltrán, C.1    Pardo, L.M.2
  • 5
    • 70350704765 scopus 로고    scopus 로고
    • Smale's 17th Problem: Average Polynomial Time to Compute Affine and Projective Solutions
    • C. Beltrán and L. M. Pardo. "Smale's 17th Problem: Average Polynomial Time to Compute Affine and Projective Solutions." J. Amer. Math. Soc. 22 (2009), 363-385.
    • (2009) J. Amer. Math. Soc. , vol.22 , pp. 363-385
    • Beltrán, C.1    Pardo, L.M.2
  • 6
    • 78651396160 scopus 로고    scopus 로고
    • Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems
    • C. Beltrán and L. M. Pardo. "Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems." Foundations of Computational Mathematics 11:1 (2011), 95-129.
    • (2011) Foundations of Computational Mathematics , vol.11 , Issue.1 , pp. 95-129
    • Beltrán, C.1    Pardo, L.M.2
  • 7
    • 75849160841 scopus 로고    scopus 로고
    • A Note on the Finite Variance of the Averaging Function for Polynomial System Solving
    • C. Beltrán and M. Shub. "A Note on the Finite Variance of the Averaging Function for Polynomial System Solving." Found. Comput. Math. 10 (2010), 115-125.
    • (2010) Found. Comput. Math. , vol.10 , pp. 115-125
    • Beltrán, C.1    Shub, M.2
  • 12
    • 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. Comp., 64:212 (1995), 1541-1555.
    • (1995) Math. Comp. , vol.64 , Issue.212 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 15
    • 80055077913 scopus 로고    scopus 로고
    • Numerical Algebraic Geometry
    • A. Leykin. "Numerical Algebraic Geometry." JSAG 3 (2011), 5-10.
    • (2011) JSAG , vol.3 , pp. 5-10
    • Leykin, A.1
  • 16
    • 67749095075 scopus 로고    scopus 로고
    • Galois Groups of Schubert Problems via Homotopy Computation
    • A. Leykin and F. Sottile. "Galois Groups of Schubert Problems via Homotopy Computation." Math. Comp. 78:267 (2009), 1749-1765.
    • (2009) Math. Comp. , vol.78 , Issue.267 , pp. 1749-1765
    • Leykin, A.1    Sottile, F.2
  • 17
    • 33746348355 scopus 로고    scopus 로고
    • Newton's Method with Deflation for Isolated Singularities of Polynomial Systems
    • A. Leykin, J. Verschelde, and A. Zhao. "Newton's Method with Deflation for Isolated Singularities of Polynomial Systems." Theoretical Computer Science 359:1-3 (2006), 111-122.
    • (2006) Theoretical Computer Science , vol.359 , Issue.1-3 , pp. 111-122
    • Leykin, A.1    Verschelde, J.2    Zhao, A.3
  • 18
    • 77950341364 scopus 로고    scopus 로고
    • Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions
    • IMA Vol. Math. Appl. Springer
    • A. Leykin, J. Verschelde, and A. Zhao. "Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions." In Algorithms in Algebraic Geometry, IMA Vol. Math. Appl. 146, pp. 79-97. Springer, 2008.
    • (2008) Algorithms in Algebraic Geometry , vol.146 , pp. 79-97
    • Leykin, A.1    Verschelde, J.2    Zhao, A.3
  • 19
    • 34248378314 scopus 로고    scopus 로고
    • How to Generate Random Matrices from the Classical Compact Groups
    • F. Mezzadri. "How to Generate Random Matrices from the Classical Compact Groups." Notices of the American Mathematical Society 54:5 (2007), 592-604.
    • (2007) Notices of the American Mathematical Society , vol.54 , Issue.5 , pp. 592-604
    • Mezzadri, F.1
  • 21
    • 62949144020 scopus 로고    scopus 로고
    • Complexity of Bézout's Theorem. VI: Geodesics in the Condition (Number) Metric
    • M. Shub. "Complexity of Bézout's Theorem. VI: Geodesics in the Condition (Number) Metric." Found. Comput. Math. 9:2 (2009), 171-178.
    • (2009) Found. Comput. Math. , vol.9 , Issue.2 , pp. 171-178
    • Shub, M.1
  • 22
    • 84968505377 scopus 로고
    • Complexity of Bézout's Theorem. I. Geometric Aspects
    • M. Shub and S. Smale. "Complexity of Bézout's Theorem. I. Geometric Aspects." J. Amer. Math. Soc. 6:2 (1993), 459-501.
    • (1993) J. Amer. Math. Soc. , vol.6 , Issue.2 , pp. 459-501
    • Shub, M.1    Smale, S.2
  • 23
    • 0028516294 scopus 로고
    • Complexity of Bézout's Theorem. V. Polynomial Time
    • Selected papers of the Workshop on Continuous Algorithms and Complexity (Barcelona, 1993)
    • M. Shub and S. Smale. "Complexity of Bézout's Theorem. V. Polynomial Time." Theoret. Comput. Sci. 133:1 (1994), Selected papers of the Workshop on Continuous Algorithms and Complexity (Barcelona, 1993), 141-164.
    • (1994) Theoret. Comput. Sci. , vol.133 , Issue.1 , pp. 141-164
    • Shub, M.1    Smale, S.2
  • 26
    • 0034580750 scopus 로고    scopus 로고
    • Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
    • 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 (2001), 2022-2046.
    • (2001) SIAM J. Numer. Anal. , vol.38 , Issue.6 , pp. 2022-2046
    • Sommese, A.J.1    Verschelde, J.2    Wampler, C.W.3
  • 27
    • 0001656792 scopus 로고    scopus 로고
    • Algorithm 795: PHCpack: A General-Purpose Solver for Polynomial Systems by Homotopy Continuation
    • J. Verschelde. "Algorithm 795: PHCpack: A General-Purpose Solver for Polynomial Systems by Homotopy Continuation." ACM Trans. Math. Softw. 25:2 (1999), 251-276.
    • (1999) ACM Trans. Math. Softw. , vol.25 , Issue.2 , pp. 251-276
    • Verschelde, J.1
  • 28
    • 21344479064 scopus 로고
    • Random Unitary Matrices
    • English summary
    • K. Zyczkowski and M. Kus. "Random Unitary Matrices" (English summary). J. Phys. A 133:27 (1994), 4235-4245.
    • (1994) J. Phys. A , vol.133 , Issue.27 , pp. 4235-4245
    • Zyczkowski, K.1    Kus, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.