메뉴 건너뛰기




Volumn 9, Issue 1, 2009, Pages 1-50

Deformation techniques for sparse systems

Author keywords

Complexity; Geometric solutions; Mixed volume; Newton Hensel lifting; Non Archimedean height; Polyhedral deformations; Probabilistic algorithms; Puiseux expansions of space curves; Sparse system solving; Symbolic homotopy algorithms

Indexed keywords

COMPLEXITY; HOMOTOPY ALGORITHMS; MIXED VOLUME; NEWTON-HENSEL LIFTING; NON-ARCHIMEDEAN HEIGHT; PROBABILISTIC ALGORITHM; SPACE CURVE; SPARSE SYSTEMS;

EID: 58849154685     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-008-9024-2     Document Type: Article
Times cited : (36)

References (61)
  • 4
    • 0005478995 scopus 로고
    • The complexity of partial derivatives
    • W. Baur V. Strassen 1983 The complexity of partial derivatives Theor. Comput. Sci. 22 317 330
    • (1983) Theor. Comput. Sci. , vol.22 , pp. 317-330
    • Baur, W.1    Strassen, V.2
  • 5
    • 34250406508 scopus 로고
    • The number of roots of a system of equations
    • D.N. Bernstein 1975 The number of roots of a system of equations Funct. Anal. Appl. 9 183 185
    • (1975) Funct. Anal. Appl. , vol.9 , pp. 183-185
    • Bernstein, D.N.1
  • 10
    • 21844434668 scopus 로고    scopus 로고
    • Polynomial evaluation and interpolation on special sets of points
    • 4
    • A. Bostan E. Schost 2005 Polynomial evaluation and interpolation on special sets of points J. Complexity 21 4 420 446
    • (2005) J. Complexity , vol.21 , pp. 420-446
    • Bostan, A.1    Schost, E.2
  • 16
    • 41549114724 scopus 로고    scopus 로고
    • A concise proof of the Kronecker polynomial system solver from scratch
    • in press. doi: 10.1016/j.expmath.2007.07.001
    • C. Durvye, G. Lecerf, A concise proof of the Kronecker polynomial system solver from scratch, Exp. Math. (2006, in press). doi: 10.1016/j.expmath.2007. 07.001.
    • (2006) Exp. Math.
    • Durvye, C.1    Lecerf, G.2
  • 17
    • 0000348667 scopus 로고
    • Efficient incremental algorithms for the sparse resultant and the mixed volume
    • I.Z. Emiris J. Canny 1995 Efficient incremental algorithms for the sparse resultant and the mixed volume J. Symb. Comput. 20 117 149
    • (1995) J. Symb. Comput. , vol.20 , pp. 117-149
    • Emiris, I.Z.1    Canny, J.2
  • 22
    • 0035294718 scopus 로고    scopus 로고
    • A Gröbner free alternative for polynomial system solving
    • 1
    • M. Giusti G. Lecerf B. Salvy 2001 A Gröbner free alternative for polynomial system solving J. Complex. 17 1 154 211
    • (2001) J. Complex. , vol.17 , pp. 154-211
    • Giusti, M.1    Lecerf, G.2    Salvy, B.3
  • 24
    • 21844450306 scopus 로고    scopus 로고
    • Intersection theory and deformation algorithms
    • Manuscript, Universidad de Buenos Aires
    • J. Heintz, G. Jeronimo, J. Sabia, P. Solernó, Intersection theory and deformation algorithms. The multihomogeneous case, Manuscript, Universidad de Buenos Aires, 2002.
    • (2002) The Multihomogeneous Case
    • J. Heintz1
  • 25
    • 0001787593 scopus 로고    scopus 로고
    • Deformation techniques for efficient polynomial equation solving
    • 1
    • J. Heintz T. Krick S. Puddu J. Sabia A. Waissbein 2000 Deformation techniques for efficient polynomial equation solving J. Complex. 16 1 70 109
    • (2000) J. Complex. , vol.16 , pp. 70-109
    • Heintz, J.1    Krick, T.2    Puddu, S.3    Sabia, J.4    Waissbein, A.5
  • 26
    • 84968520678 scopus 로고
    • A polyhedral method for solving sparse polynomial systems
    • 212
    • B. Huber B. Sturmfels 1995 A polyhedral method for solving sparse polynomial systems Math. Comput. 64 212 1541 1555
    • (1995) Math. Comput. , vol.64 , pp. 1541-1555
    • Huber, B.1    Sturmfels, B.2
  • 29
    • 0002615049 scopus 로고
    • Newton polyhedra and the genus of complete intersections
    • A.G. Khovanski 1978 Newton polyhedra and the genus of complete intersections Funct. Anal. Appl. 12 38 46
    • (1978) Funct. Anal. Appl. , vol.12 , pp. 38-46
    • Khovanski, A.G.1
  • 30
    • 0039930339 scopus 로고
    • Newton polytopes and the Bézout theorem
    • A.G. Kushnirenko 1976 Newton polytopes and the Bézout theorem Funct. Anal. Appl. 10 233 235
    • (1976) Funct. Anal. Appl. , vol.10 , pp. 233-235
    • Kushnirenko, A.G.1
  • 31
    • 0041459777 scopus 로고    scopus 로고
    • Quadratic Newton iteration for systems with multiplicity
    • 3
    • G. Lecerf 2002 Quadratic Newton iteration for systems with multiplicity Found. Comput. Math. 2 3 247 293
    • (2002) Found. Comput. Math. , vol.2 , pp. 247-293
    • Lecerf, G.1
  • 32
    • 0042156945 scopus 로고    scopus 로고
    • Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers
    • 4
    • G. Lecerf 2003 Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers J. Complex. 19 4 564 596
    • (2003) J. Complex. , vol.19 , pp. 564-596
    • Lecerf, G.1
  • 33
    • 0012316556 scopus 로고    scopus 로고
    • Finding mixed cells in the mixed volume computation
    • 2
    • T.-Y. Li X. Li 2001 Finding mixed cells in the mixed volume computation Found. Comput. Math. 1 2 161 181
    • (2001) Found. Comput. Math. , vol.1 , pp. 161-181
    • Li, T.-Y.1    Li, X.2
  • 34
    • 85011518993 scopus 로고    scopus 로고
    • Numerical solution of multivariate polynomial systems by homotopy continuation methods
    • T.Y. Li 1997 Numerical solution of multivariate polynomial systems by homotopy continuation methods Acta Numer. 6 399 436
    • (1997) Acta Numer. , vol.6 , pp. 399-436
    • Li, T.Y.1
  • 36
    • 2042436402 scopus 로고    scopus 로고
    • High probability analysis of the condition number of sparse polynomial systems
    • 2-3
    • G. Malajovich J.M. Rojas 2004 High probability analysis of the condition number of sparse polynomial systems Theor. Comput. Sci. 315 2-3 525 555
    • (2004) Theor. Comput. Sci. , vol.315 , pp. 525-555
    • Malajovich, G.1    Rojas, J.M.2
  • 38
    • 0000376595 scopus 로고
    • A generic product-decomposition formula for Bézout numbers
    • A. Morgan A. Sommese C. Wampler 1995 A generic product-decomposition formula for Bézout numbers SIAM J. Numer. Anal. 32 1308 1325
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1308-1325
    • Morgan, A.1    Sommese, A.2    Wampler, C.3
  • 41
    • 2042437053 scopus 로고    scopus 로고
    • Deformation techniques to solve generalized Pham systems
    • 2-3
    • L.M. Pardo J. San Martín 2004 Deformation techniques to solve generalized Pham systems Theoret. Comput. Sci. 315 2-3 593 625
    • (2004) Theoret. Comput. Sci. , vol.315 , pp. 593-625
    • Pardo, L.M.1    San Martín, J.2
  • 42
    • 51249161636 scopus 로고
    • Product formulas for resultants and Chow forms
    • 3
    • P. Pedersen B. Sturmfels 1993 Product formulas for resultants and Chow forms Math. Z. 214 3 377 396
    • (1993) Math. Z. , vol.214 , pp. 377-396
    • Pedersen, P.1    Sturmfels, B.2
  • 43
    • 44249090060 scopus 로고    scopus 로고
    • Hauteur normalisée des variétés toriques projectives
    • in press. doi: 10.1017/S1474748007000138,35pp.,eprintmath.NT/0406476
    • P. Philippon, M. Sombra, Hauteur normalisée des variétés toriques projectives, J. Inst. Math. Jussieu (2003, in press). doi: 10.1017/S1474748007000138, 35pp., eprint math.NT/0406476.
    • (2003) J. Inst. Math. Jussieu
    • Philippon, P.1    Sombra, M.2
  • 44
    • 15944399682 scopus 로고    scopus 로고
    • Géométrie Diophantienne et variétés toriques
    • P. Philippon M. Sombra 2005 Géométrie Diophantienne et variétés toriques C. R. Math. Acad. Sci. Paris 340 507 512
    • (2005) C. R. Math. Acad. Sci. Paris , vol.340 , pp. 507-512
    • Philippon, P.1    Sombra, M.2
  • 46
    • 0001332639 scopus 로고    scopus 로고
    • Solving degenerate sparse polynomial systems faster
    • 1/2
    • J.M. Rojas 1999 Solving degenerate sparse polynomial systems faster J. Symbolic Comput. 28 1/2 155 186
    • (1999) J. Symbolic Comput. , vol.28 , pp. 155-186
    • Rojas, J.M.1
  • 49
    • 0030163190 scopus 로고    scopus 로고
    • Counting affine roots of polynomial systems via pointed Newton polytopes
    • 2
    • J.M. Rojas X. Wang 1996 Counting affine roots of polynomial systems via pointed Newton polytopes J. Complex. 12 2 116 133
    • (1996) J. Complex. , vol.12 , pp. 116-133
    • Rojas, J.M.1    Wang, X.2
  • 50
    • 0000874914 scopus 로고    scopus 로고
    • Bounds for traces in complete intersections and degrees in the Nullstellensatz
    • 6
    • J. Sabia P. Solernó 1996 Bounds for traces in complete intersections and degrees in the Nullstellensatz Appl. Algebra Eng. Commun. Comput. 6 6 353 376
    • (1996) Appl. Algebra Eng. Commun. Comput. , vol.6 , pp. 353-376
    • Sabia, J.1    Solernó, P.2
  • 52
    • 0037332265 scopus 로고    scopus 로고
    • Computing parametric geometric resolutions
    • E. Schost 2003 Computing parametric geometric resolutions Appl. Algebra Eng. Commun. Comput. 13 349 393
    • (2003) Appl. Algebra Eng. Commun. Comput. , vol.13 , pp. 349-393
    • Schost, E.1
  • 56
    • 0039648503 scopus 로고    scopus 로고
    • Mixed volume computation by dynamic lifting applied to polynomial system solving
    • 1
    • J. Verschelde K. Gatermann R. Cools 1996 Mixed volume computation by dynamic lifting applied to polynomial system solving Discrete Comput. Geom. 16 1 69 112
    • (1996) Discrete Comput. Geom. , vol.16 , pp. 69-112
    • Verschelde, J.1    Gatermann, K.2    Cools, R.3
  • 57
    • 0028449799 scopus 로고
    • Homotopies exploiting Newton polytopes for solving sparse polynomial systems
    • 3
    • J. Verschelde P. Verlinden R. Cools 1994 Homotopies exploiting Newton polytopes for solving sparse polynomial systems SIAM J. Numer. Anal. 31 3 915 930
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 915-930
    • Verschelde, J.1    Verlinden, P.2    Cools, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.