A new extension of Hermite matrix polynomials and its applications
type: Item
instance of: scholarly article
title: A new extension of Hermite matrix polynomials and its applications
zbMATH Open document ID: 1106.15016
author: Raed S. Batahan
published in: Linear Algebra and its Applications
publication date: 2006-12-07T00:00:00Z
review text: A two-variable extension of Hermite matrix polynomials is introduced and studied. It is proved that these matrix polynomials satisfy some recurrence relations and appear as finite series solution of matrix differential equations. The two-variable Hermite matrix polynomials series expansion of \(\exp(Ax)\), \(\sin(Ax)\) and \(\cos(Ax)\) for a matrix \(A \in {\mathbb C}^{N \times N}\), that satisfies an appropriate spectral property, is given. The Rodrigues' formula of two-variable Hermite matrix polynomials is presented. Finally, by using this family of matrix polynomials the Chebyshev matrix polynomials of the second kind are defined.
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 5077729
zbMATH Keywords: Hermite matrix polynomials
zbMATH Keywords: Chebyshev matrix polynomials
zbMATH Keywords: Rodrigues' formula
zbMATH Keywords: three terms recurrence relation
zbMATH Keywords: matrix differential equations
MaRDI profile type: Publication
full work available at URL: j.laa.2006.04.006
OpenAlex ID: W2050591671
cites work: Stable numerical solution of strongly coupled mixed diffusion problems
cites work: Q3848301
cites work: Some applications of the Hermite matrix polynomials series expansions
cites work: Q3153471
cites work: Q4890865
cites work: Laguerre matrix polynomials and systems of second-order differential equations
cites work: Q4399285
cites work: Q4881582
cites work: Analytic and numerical solution of coupled implicit semi-infinite diffusion problems
cites work: Explicit solution of time dependent diffusion problems in a semi-infinite medium.
cites work: On generalized Hermite matrix polynomials
cites work: Q5488405
DOI: 10.1016/J.LAA.2006.04.006
description: scientific article; zbMATH DE number 5077729