Approximate square-free decomposition and root-finding of lll-conditioned algebraic equations
Journal of Information Processing
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Applied numerical linear algebra
Applied numerical linear algebra
Optimization strategies for the approximate GCD problem
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
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Computation of approximate polynomial GCDs and an extension
Information and Computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Computing Approximate GCDs in Ill-conditioned Cases
Proceedings of the 2007 international workshop on Symbolic-numeric computation
An iterative method for calculating approximate GCD of univariate polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
IEEE Transactions on Signal Processing
QR factoring to compute the GCD of univariate approximate polynomials
IEEE Transactions on Signal Processing
GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials
ACM Communications in Computer Algebra
GPGCD: An iterative method for calculating approximate GCD of univariate polynomials
Theoretical Computer Science
Calculating approximate GCD of multiple univariate polynomials using approximate syzygies
ACM Communications in Computer Algebra
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We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transferred to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input.