Factoring rational polynomials over the complex numbers
SIAM Journal on Computing
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
A numerical absolute primality test for bivariate polynomials
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic 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
Challenges of symbolic computation: my favorite open problems
Journal of Symbolic Computation
Pseudofactors of multivariate polynomials
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Approximate multivariate polynomial factorization based on zero-sum relations
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
SIAM Journal on Numerical Analysis
Polynomial Factorization 1987-1991
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On approximate irreducibility of polynomials in several variables
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Approximate factorization of multivariate polynomials via differential equations
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
Symbolic-numeric sparse interpolation of multivariate polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
On Location and Approximation of Clusters of Zeros: Case of Embedding Dimension One
Foundations of Computational Mathematics
From an approximate to an exact absolute polynomial factorization
Journal of Symbolic Computation
Extracting numerical factors of multivariate polynomials from taylor expansions
Proceedings of the 2009 conference on Symbolic numeric computation
Continuations and monodromy on random riemann surfaces
Proceedings of the 2009 conference on Symbolic numeric computation
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Computing monodromy via continuation methods on random Riemann surfaces
Theoretical Computer Science
Roots of the derivatives of some random polynomials
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
| Hi-index | 0.00 |
We briefly present and analyze, from a geometric viewpoint, strategies for designing algorithms to factor bivariate approximate polynomials in C[x; y]. Given a composite polynomial, stably square-free, satisfying a genericity hypothesis, we describe the effect of a perturbation on the roots of its discriminant with respect to one variable, and the perturbation of the corresponding monodromy action on a smooth fiber. A novel geometric approach is presented, based on guided projection in the parameter space and continuation method above randomly chosen loops, to reconstruct from a perturbed polynomial a nearby composite polynomial and its irreducible factors. An algorithm and its ingredients are described.