Homotopies exploiting Newton polytopes for solving sparse polynomial systems
SIAM Journal on Numerical Analysis
A polyhedral method for solving sparse polynomial systems
Mathematics of Computation
Complexity and real computation
Complexity and real computation
Efficient algorithms for computing the nearest polynomial with a real root and related problems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Toric Newton method for polynomial homotopies
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Absolute polynomial factorization in two variables and the knapsack problem
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
A Rank-Revealing Method with Updating, Downdating, and Applications
SIAM Journal on Matrix Analysis and Applications
Symbolic-numeric sparse interpolation of multivariate polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On the frontiers of polynomial computations in tropical geometry
Journal of Symbolic Computation
Journal of Symbolic Computation
Approximate bivariate factorization: a geometric viewpoint
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing monodromy groups defined by plane algebraic curves
Proceedings of the 2007 international workshop on Symbolic-numeric computation
A numerical study of extended Hensel series
Proceedings of the 2007 international workshop on Symbolic-numeric computation
From quotient-difference to generalized eigenvalues and sparse polynomial interpolation
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Journal of Symbolic Computation
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
Good reduction of puiseux series and complexity of the Newton-Puiseux algorithm over finite fields
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
A new algorithm for sparse interpolation of multivariate polynomials
Theoretical Computer Science
Deformation Techniques for Sparse Systems
Foundations of Computational Mathematics
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Computing Puiseux series for algebraic surfaces
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view of this problem leads to efficient preprocessing techniques, applying polyhedral methods to the exact exponents and numerical techniques to the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry.