Fast parallel absolute irreducibility testing
Journal of Symbolic Computation
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
Riemann surfaces, plane algebraic curves and their period matrices
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
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
Semi-numerical determination of irreducible branches of a reduced space curve
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
Irreducible decomposition of curves
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
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
Towards certified irreducibility testing of bivariate approximate 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
A method computing multiple roots of inexact polynomials
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Absolute polynomial factorization in two variables and the knapsack problem
ISSAC '04 Proceedings of the 2004 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
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Towards more accurate separation bounds of empirical polynomials II
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Extracting numerical factors of multivariate polynomials from taylor expansions
Proceedings of the 2009 conference on Symbolic numeric computation
Approximate factorization of polynomials over Z
Proceedings of the 2009 conference on Symbolic numeric computation
Parametrization of ε-rational curves: extended abstract
Proceedings of the 2009 conference on Symbolic numeric computation
Polynomial datapath optimization using partitioning and compensation heuristics
Proceedings of the 46th Annual Design Automation Conference
Improved heuristics for finite word-length polynomial datapath optimization
Proceedings of the 2009 International Conference on Computer-Aided Design
Approximate parametrization of plane algebraic curves by linear systems of curves
Computer Aided Geometric Design
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Modular datapath optimization and verification based on modular-HED
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Diversification improves interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Polynomial datapath optimization using constraint solving and formal modelling
Proceedings of the International Conference on Computer-Aided Design
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We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that contain numerical noise. Our algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss-Newton optimization to numerically compute the approximate multivariate factors. We demonstrate on a large set of benchmark polynomials that our algorithms efficiently yield approximate factorizations within the coefficient noise even when the relative error in the input is substantial (10^-^3).