Algorithms for computer algebra
Algorithms for computer algebra
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
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On approximate GCDs of univariate polynomials
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Solving some overdetermined polynomial systems
ISSAC '99 Proceedings of the 1999 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
Polynomial Factorization 1987-1991
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
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
Quantified constraints under perturbation
Journal of Symbolic 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
Computer algebra handbook
Approximate factorization of multivariate polynomials via differential equations
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
Approximate bivariate factorization: a geometric viewpoint
Proceedings of the 2007 international workshop on Symbolic-numeric computation
On real factors of real interval polynomials
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
On real factors of real interval polynomials
Journal of Symbolic Computation
Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm
International Journal of Computational Science and Engineering
Extracting numerical factors of multivariate polynomials from taylor expansions
Proceedings of the 2009 conference on Symbolic numeric computation
Finding exact minimal polynomial by approximations
Proceedings of the 2009 conference on Symbolic numeric computation
Approximate factorization of polynomials over Z
Proceedings of the 2009 conference on Symbolic numeric computation
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We treat pseudo-factorization of a multivariate polynomial p over C as an overdetermined bilinear system for the coefficients of the factors. If the specified data (coefficients of p) are sufficiently close to the manifold of consistent data we project onto it by solving a well-chosen subsystem (otherwise we quit). On the manifold, we reduce the backward error by a linearized minimization procedure. The resulting algorithm appears to extend the range of treatable cases - in terms of number of variables and total degree - considerably.