Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials

• Autorzy: Dimitrios Christou , Marilena Mitrouli , Dimitrios Triantafyllou
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Sylvester matrix; Bézout matrix; QR decomposition; Singular value decomposition

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 202-224

Daty

wydano

2017-10-26

otrzymano

2017-06-13

zaakceptowano

2017-09-06

online

2017-10-20

Twórcy

autor

Dimitrios Christou

• ,

autor

Marilena Mitrouli

• ,,

autor

Dimitrios Triantafyllou

• ,,

Identyfikatory

DOI

10.1515/spma-2017-0015