Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials

Dimitrios Christou, Marilena Mitrouli, and Dimitrios Triantafyllou. "Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials." Special Matrices 5.1 (2017): 202-224. <http://eudml.org/doc/288571>.

@article{DimitriosChristou2017,
abstract = {This paper revisits the Bézout, Sylvester, and power-basis matrix representations of the greatest common divisor (GCD) of sets of several polynomials. Furthermore, the present work introduces the application of the QR decomposition with column pivoting to a Bézout matrix achieving the computation of the degree and the coeffcients of the GCD through the range of the Bézout matrix. A comparison in terms of computational complexity and numerical effciency of the Bézout-QR, Sylvester-QR, and subspace-SVD methods for the computation of theGCDof sets of several polynomials with real coeffcients is provided.Useful remarks about the performance of the methods based on computational simulations of sets of several polynomials are also presented.},
author = {Dimitrios Christou, Marilena Mitrouli, Dimitrios Triantafyllou},
journal = {Special Matrices},
keywords = {Sylvester matrix; Bézout matrix; QR decomposition; Singular value decomposition},
language = {eng},
number = {1},
pages = {202-224},
title = {Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials},
url = {http://eudml.org/doc/288571},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Dimitrios Christou
AU - Marilena Mitrouli
AU - Dimitrios Triantafyllou
TI - Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials
JO - Special Matrices
PY - 2017
VL - 5
IS - 1
SP - 202
EP - 224
AB - This paper revisits the Bézout, Sylvester, and power-basis matrix representations of the greatest common divisor (GCD) of sets of several polynomials. Furthermore, the present work introduces the application of the QR decomposition with column pivoting to a Bézout matrix achieving the computation of the degree and the coeffcients of the GCD through the range of the Bézout matrix. A comparison in terms of computational complexity and numerical effciency of the Bézout-QR, Sylvester-QR, and subspace-SVD methods for the computation of theGCDof sets of several polynomials with real coeffcients is provided.Useful remarks about the performance of the methods based on computational simulations of sets of several polynomials are also presented.
LA - eng
KW - Sylvester matrix; Bézout matrix; QR decomposition; Singular value decomposition
UR - http://eudml.org/doc/288571
ER -