Some explicit formulas for the polynomial decomposition of the matrix exponential and applications
type: Item
instance of: scholarly article
title: Some explicit formulas for the polynomial decomposition of the matrix exponential and applications
zbMATH Open document ID: 1003.15021
DOI: 10.1016/S0024-3795(02)00271-9
author: R. Ben Taher
author: M. Rachidi
published in: Linear Algebra and its Applications
publication date: 2002-08-28T00:00:00Z
review text: Formulas for the polynomial decomposition of the exponential of a square matrix \(A\), by considering the Jordan normal form of \(A\), are studied. The exponential \(e^{iA}\) is given in terms of \(P_0(A),\dots,P_{m-1} (A) \), where the \(P_j(A)\) are polynomials in \(A\) of degree less than \(m\). The cases with \(m=5\) and \(m=6\) are discussed in detail. The results are also compared with those derived by the authors previously [ibid. 330, No. 1-3, 15-24 (2001; Zbl 0983.15018)].
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 40A25
zbMATH DE Number: 1790263
zbMATH Keywords: matrix polynomial decomposition
zbMATH Keywords: matrix exponential
zbMATH Keywords: powers of a matrix
zbMATH Keywords: convergence of a series
zbMATH Keywords: summation of series
zbMATH Keywords: Jordan normal form
MaRDI profile type: Publication
cites work: Some Explicit Formulas for the Exponential Matrix e tA
cites work: Linear recurrence relations in the algebra of matrices and applications
cites work: Some explicit formulas for the matrix exponential
cites work: More explicit formulas for the matrix exponential
cites work: Q4347569
cites work: Q3898560
cites work: Q3254327
cites work: Q4000373
cites work: Q3691740
cites work: Q3990995
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix
cites work: Q4936061
cites work: \(r\)-generalized Fibonacci sequences, Cayley-Hamilton theorem and Markov chains
cites work: Q3795726
cites work: Q4313233
full work available at URL: s0024-3795(02)00271-9
OpenAlex ID: W2050150425
description: scientific article; zbMATH DE number 1790263