Displaying similar documents to “Comparison of algorithms for calculation of the greatest common divisor of several polynomials”

Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials

Dimitrios Christou, Marilena Mitrouli, Dimitrios Triantafyllou (2017)

Special Matrices

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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,...

On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis (2015)

Serdica Journal of Computing

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In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell...

Factorization makes fast Walsh, PONS and other Hadamard-like transforms easy

Kautsky, Jaroslav

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A simple device, based on the factorization of invertible matrix polynomials, enabling to identify the possibility of fast implementation of linear transforms is presented. Its applicability is demonstrated in the case of Hadamard matrices and their generalization, Hadamard matrix polynomials.

A fixed point method to compute solvents of matrix polynomials

Fernando Marcos, Edgar Pereira (2010)

Mathematica Bohemica

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Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.