Approximate factorization of multivariable polynomials
Signal Processing
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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
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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
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
Towards more accurate separation bounds of empirical polynomials
ACM SIGSAM Bulletin
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation
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Extracting numerical factors of multivariate polynomials from taylor expansions
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Approximate factorization of polynomials over Z
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Towards more accurate separation bounds of empirical polynomials II
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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Let F(x, u) be a given bivariate polynomial and ε be a small positive number. We consider the approximate factorization of F: find polynomials G, H and ΔF such that F = GH + ΔF and ‖ΔF‖ / ‖F‖= ε, where ‖P‖ denotes 2-norm of polynomial P. At first, we introduce a relation between the irreducibility of F and the singular value of a certain matrix. By this relation and an upper bound of variations of the power-series roots of a bivariate polynomial, we give an algorithm for an absolute irreducibility test of a polynomial whose coefficients are perturbed within a given tolerance. In addition, we give a lower bound for a tolerance of the approximate factorization of a given bivariate polynomial. The lower bound is the necessary magnitude of perturbations which make a given polynomial reducible.