Displaying similar documents to “Construction of algebraic and difference equations with a prescribed solution space”

On the coefficients of the max-algebraic characteristic polynomial and equation

Peter Butkovič (2003)

Kybernetika

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No polynomial algorithms are known for finding the coefficients of the characteristic polynomial and characteristic equation of a matrix in max- algebra. The following are proved: (1) The task of finding the max-algebraic characteristic polynomial for permutation matrices encoded using the lengths of their constituent cycles is NP-complete. (2) The task of finding the lowest order finite term of the max-algebraic characteristic polynomial for a { 0 , - ∞ } matrix can be converted to the assignment...

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.

Infinite elementary divisor structure-preserving transformations for polynomial matrices

Nicholas Karampetakis, Stavros Vologiannidis (2003)

International Journal of Applied Mathematics and Computer Science

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The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where...

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.