Displaying similar documents to “Some relations on Humbert matrix polynomials”

Some relations satisfied by Hermite-Hermite matrix polynomials

Ayman Shehata, Lalit Mohan Upadhyaya (2017)

Mathematica Bohemica

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The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the...

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 Hermite-Hermite matrix polynomials

M. S. Metwally, M. T. Mohamed, A. Shehata (2008)

Mathematica Bohemica

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In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite matrix polynomials is proposed.

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.

Relations between the orthogonal matrix polynomials on [a, b], Dyukarev-Stieltjes parameters, and Schur complements

A.E. Choque-Rivero (2017)

Special Matrices

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We obtain explicit interrelations between new Dyukarev-Stieltjes matrix parameters and orthogonal matrix polynomials on a finite interval [a, b], as well as the Schur complements of the block Hankel matrices constructed through the moments of the truncated Hausdorff matrix moment (THMM) problem in the nondegenerate case. Extremal solutions of the THMM problem are described with the help of matrix continued fractions.