Letter to the Editor: Computing multiple integrals involving matrix exponentials

Authors:
F. Carbonell;J. C. Jímenez;L. M. Pedroso
Affiliations:
Departamento de Matemática Interdisciplinaria, Instituto de Cibernética, Matemática y Física, Calle 15, No. 551, e/ C y D, Vedado, La Habana 4, C.P. 10400, Cuba;Departamento de Matemática Interdisciplinaria, Instituto de Cibernética, Matemática y Física, Calle 15, No. 551, e/ C y D, Vedado, La Habana 4, C.P. 10400, Cuba;Departamento de Matemática Interdisciplinaria, Instituto de Cibernética, Matemática y Física, Calle 15, No. 551, e/ C y D, Vedado, La Habana 4, C.P. 10400, Cuba
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, a generalization of a formula proposed by Van Loan [Computing integrals involving the matrix exponential, IEEE Trans. Automat. Control 23 (1978) 395-404] for the computation of multiple integrals of exponential matrices is introduced. In this way, the numerical evaluation of such integrals is reduced to the use of a conventional algorithm to compute matrix exponentials. The formula is applied for evaluating some kinds of integrals that frequently emerge in a number classical mathematical subjects in the framework of differential equations, numerical methods and control engineering applications.