scholarly journals Study on a Generalized Bezout Matrix

2014 ◽  
Vol 03 (02) ◽  
pp. 98-103
Author(s):  
井鹏 孙
Keyword(s):  
Bezout Matrix

scholarly journals Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials

2017 ◽  
Vol 5 (1) ◽  
pp. 202-224 ◽  
Author(s):  
Dimitrios Christou ◽  
Marilena Mitrouli ◽  
Dimitrios Triantafyllou
Keyword(s):  
Computational Complexity ◽  
Qr Decomposition ◽  
Greatest Common Divisor ◽  
Computational Simulations ◽  
Matrix Representations ◽  
Basis Matrix ◽  
Matrix Methods ◽  
Structured Matrix ◽  
Bezout Matrix ◽  
Column Pivoting

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.

scholarly journals The Bézout matrix for Hermite interpolants

2015 ◽  
Vol 474 ◽  
pp. 12-29
Author(s):  
D.A. Aruliah ◽  
R.M. Corless ◽  
G.M. Diaz-Toca ◽  
L. Gonzalez-Vega ◽  
A. Shakoori
Keyword(s):  
Bezout Matrix

The GPGCD algorithm with the Bézout matrix

2019 ◽  
Vol 53 (3) ◽  
pp. 99-102
Author(s):  
Boming Chi ◽  
Akira Terui
Keyword(s):  
Bezout Matrix
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