E. Kaltofen, Polynomial factorization: a success story, Proc. of ISSAC’03, ACM Press (2003), 3–4.
E. Kaltofen, Challenges of symbolic computation: My favorite open problems, J. Symb. Comput., 29 (2000), 161–168.
L. Blum, F. Cucker, M. Shub and S. Smale, Complexity and Real Computation, Springer-Verlag, New York, 1998.
J.-P. Dedieu and M. Shub, Newton’s method for overdetermined system of equations, Mathematics of Computation 69 (2002), 1099–1115.
S. Smale, Newton’s method estimates from data at one point, in The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics (R. Ewing, K. Gross, and C. Martin, eds.), Springer-Verlag, New York, 1986, pp. 185–196.
Z. Zeng, Computing multiple roots of inexact polynomials, Math. Comp., 74 (2005), 869–903.
P. Bürgisser and F. Cucker, Condition: The Geometry of Numerical Algorithms, Series: Grundlehren der mathematischen Wissenschaften 349, Springer, 2013.
W. Kahan, Conserving confluence curbs ill-condition, Technical Report, Computer Science Department, University of California, Berkeley, 1972.
D.J. Bates, J.D. Hauenstein, A.J. Sommese and C.W. Wampler, Numerically Solving Polynomial Systems with Bertini, SIAM Publications, 2013.
T.Y. Li, Solving polynomial systems by the homotopy continuation method, in Handbook of Numerical Analysis Vol. XI (P.G. Ciarlet, J.L. Lions eds.), Elsevier B.V. 2003, pp. 209–304.
R. Corless, M. Giesbrecht, M. Van Hoeij, I. Kotsireas and S. Watt, Towards Factoring bivariate Approximate Polynomials, Proc. of ISSAC’01, ACM Press (2001), 85–92.
R. Corless, A. Galligo, I. Kotsireas and S. Watt, A geometric-numeric algorithm for absolute factorization of multivariate polynomials, Proc. of ISSAC’02, ACM Press (2002), 37–45.
A. Galligo and M. van Hoeij, Approximate bivariate factorization, a geometric viewpoint, Proceedings of SNC’07, ACM Press (2007), 1–10.
Z. Zeng, Regularization and matrix computation in numerical polynomial algebra, in Approximate Commutative Algebra, Texts and Monographs in Symbolic Computation (L. Robbiano, and J. Abbott eds.), Springer Vienna, 2009, pp. 125–162.
T. Sasaki, M. Suzuki, M. Kolar, and M. Sasaki, Approximate factorization of multivariate polynomials and absolute irreducibility testing, Japan Journal of Industrial and Applied Mathematics, 8–3 (1991), 357–375.
M. van Hoeij, Factoring polynomials and the knapsack problem, Journal of Number Theory, 95–2 (2002), 167–189.
A. Lenstra, H. Lenstra, and L. Lovasz, Factoring polynomials with rational coefficients, Mathematische Annalen, 261–4 (1982), 515–534.
J. von zur Gathen and E. Kaltofen, Factoring sparse multivariate polynomials, Journal of Computer and System Sciences, 31–2 (1985), 265–287.
E. Kaltofen, Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization, SIAM Journal on Computing, 14–2 (1985), 469–489.
G. Lecerf, New recombination algorithms for bivariate polynomial factorization based on Hensel lifting, Applicable Algebra in Engineering, Communication and Computing, 21–2 (2010), 151–176.
Y. Huang, H.J. Stetter, W. Wu and L. Zhi, Pseudofactors of multivariate polynomials, Proc. of ISSAC’00, ACM Press (2000), 161–168.
A. Galligo and S. Watt, A numerical absolute primality test for bivariate polynomials, Proceedings of ISSAC’97, ACM Press (1997), 217–224.
E. Kaltofen and J. May, On approximate irreducibility of polynomials in several variables, Proc. of ISSAC’03, ACM Press (2003), 161–168.
T. Sasaki, Approximate multivariate polynomial factorization based on zero-sum relations, Proceedings of ISSAC 2001 ACM Press (2001), 284–291.
S. Gao, E. Kaltofen, J. May, Z. Yang and L. Zhi, Approximate factorization of multivariate polynomials via differential equations, Proc. of ISSAC’04, ACM Press (2004), 167–174.
A. Sommese, J. Verschelde and C. Wampler, Numerical factorization of multivariate complex polynomials, Theoret. Comput. Sci. 315 (2004), 651–669.
J. Verschelde, Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation, ACM Trans. Math. Softw. 25–2 (1999), 251–276.
W. Ruppert, Reducibility of polynomials \(f(x,y)\), J. Number Theory, 77 (1999), 62–70.
S. Gao, Factoring multivariate polynomials via partial differential equations, Mathematics of Computation, 72–242 (2003), 801–822.
E. Kaltofen, J. May, Z. Yang, and L. Zhi, Approximate factorization of multivariate polynomials using singular value decomposition, J. Symb. Comput., 43–5 (2008), 359–376.
G. W. Stewart, Matrix Algorithms. Volume I: Basic Decompositions, SIAM publications, 1998.
Z. Zeng, The Gauss–Newton iteration and Tubular Neighborhood Theorem, Preprint, 2012, http://homepages.neiu.edu/~zzeng/Papers/tnt
Z. Zeng, ApaTools: A Maple and Matlab toolbox for approximate polynomial algebra, Software for Algebraic Geometry, IMA Volume 148, (M. Stillman, N. Takayama and J. Verschelde, eds.) Springer, 2008, pp. 149–167.