Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing Approximate GCDs in Ill-conditioned Cases
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Structured matrix-based methods for polynomial ∈-gcd: analysis and comparisons
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Minimum converging precision of the QR-factorization algorithm for real polynomial GCD
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A structured rank-revealing method for Sylvester matrix
Journal of Computational and Applied Mathematics
Structured total least norm and approximate GCDs of inexact polynomials
Journal of Computational and Applied Mathematics
ApaTools: a software toolbox for approximate polynomial algebra
ACM Communications in Computer Algebra
An iterative method for calculating approximate GCD of univariate polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
The approximate irreducible factorization of a univariate polynomial: revisited
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computing multivariate approximate GCD based on Barnett's theorem
Proceedings of the 2009 conference on Symbolic numeric computation
Spatially robust audio compensation based on SIMO feedforward control
IEEE Transactions on Signal Processing
Journal of Computational and Applied Mathematics
Blind image deconvolution via fast approximate GCD
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
The calculation of the degree of an approximate greatest common divisor of two polynomials
Journal of Computational and Applied Mathematics
GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
Approximate polynomial GCD over integers
Journal of Symbolic Computation
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
Extended companion matrix for approximate GCD
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Journal of Computational and Applied Mathematics
Number of zeros of interval polynomials
Journal of Computational and Applied Mathematics
Ruppert matrix as subresultant mapping
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
GPGCD: An iterative method for calculating approximate GCD of univariate polynomials
Theoretical Computer Science
Journal of Computational and Applied Mathematics
Revisiting QRGCD and comparison with ExQRGCD
ACM Communications in Computer Algebra
Newton-like iteration for determinantal systems and structured low rank approximation
ACM Communications in Computer Algebra
NAClab: a Matlab toolbox for numerical algebraic computation
ACM Communications in Computer Algebra
Hi-index | 35.69 |
We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the greatest common divisor (GCD) of univariate approximate polynomials over R[x] or C[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9.