Approximate square-free decomposition and root-finding of lll-conditioned algebraic equations
Journal of Information Processing
A bibliography on roots of polynomials
Journal of Computational and Applied Mathematics
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 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
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Computation of approximate polynomial GCDs and an extension
Information and Computation
On square-free decomposition algorithms
SYMSAC '76 Proceedings of the third ACM 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
Algorithm 835: MultRoot---a Matlab package for computing polynomial roots and multiplicities
ACM Transactions on Mathematical Software (TOMS)
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
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When multiple roots are present, factoring a univariate polynomial is an ill-posed problem in the sense that it is highly sensitive to data perturbations and the round-off error. In ISSAC '03, the author introduced an algorithm that is capable of calculating the polynomial roots and multiplicities accurately using floating point arithmetic without extending the hardware precision even if the coefficients are perturbed. This paper revisits the problem by establishing a rigorous theoretical framework for eliminating the ill-posedness and by introducing a redesigned algorithm. The new algorithm avoids error accumulation in the GCD computation and substantially improves the accuracy and robustness.