Displaying similar documents to “Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’S)”

Remarks on inverse of matrix polynomials

Fischer, Cyril, Náprstek, Jiří

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Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes...

Discrete-time symmetric polynomial equations with complex coefficients

Didier Henrion, Jan Ježek, Michael Šebek (2002)

Kybernetika

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Discrete-time symmetric polynomial equations with complex coefficients are studied in the scalar and matrix case. New theoretical results are derived and several algorithms are proposed and evaluated. Polynomial reduction algorithms are first described to study theoretical properties of the equations. Sylvester matrix algorithms are then developed to solve numerically the equations. The algorithms are implemented in the Polynomial Toolbox for Matlab.

On a Theorem by Van Vleck Regarding Sturm Sequences

Akritas, Alkiviadis, Malaschonok, Gennadi, Vigklas, Panagiotis (2013)

Serdica Journal of Computing

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In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences...

An equivalent matrix pencilfor bivariate polynomial matrices

Mohamed Boudellioua (2006)

International Journal of Applied Mathematics and Computer Science

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In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

Subresultant Polynomial Remainder Sequences Obtained by Polynomial Divisions in Q[x] or in Z[x]

Akritas, Alkiviadis G., Malaschonok, Gennadi I., Vigklas, Panagiotis S. (2016)

Serdica Journal of Computing

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In this paper we present two new methods for computing the subresultant polynomial remainder sequence (prs) of two polynomials f, g ∈ Z[x]. We are now able to also correctly compute the Euclidean and modified Euclidean prs of f, g by using either of the functions employed by our methods to compute the remainder polynomials. Another innovation is that we are able to obtain subresultant prs’s in Z[x] by employing the function rem(f, g, x) to compute the remainder polynomials in [x]. This...

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

Irina Karelin, Leonid Lerer (2001)

International Journal of Applied Mathematics and Computer Science

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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...