Computing high dimensional multiple integrals involving matrix exponentials

This paper deals with the numerical computation of the high dimensional multiple integrals involving matrix exponentials that can be rewritten as the product of a matrix exponential times vector. To this end, in addition to the conventional iterative methods for computing the action of the matrix ex...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 421; p. 114844
Main Authors: Naranjo-Noda, F.S., Jimenez, J.C.
Format: Journal Article
Language:English
Published: Elsevier B.V 15.03.2023
Subjects:
Krylov-subspace
Matrix exponential
Multiple integral
Phi-function
Krylov-subspace
Multiple integral
Phi-function
Matrix exponential
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:This paper deals with the numerical computation of the high dimensional multiple integrals involving matrix exponentials that can be rewritten as the product of a matrix exponential times vector. To this end, in addition to the conventional iterative methods for computing the action of the matrix exponential on a vector, iterative methods for the action of the phi-function over a vector are also considered. This is illustrated with a Krylov–Padé approximation to the product of phi-function times vector, which reveals potential for computing a variety of high dimensional multiple integrals that arise in several areas of applied mathematics, model identification, control engineering and numerical methods. •Computation of high dimensional multiple integrals involving matrix exponentials.•High order Krylov–Padé approximation for the action of the matrix exponential.•Error-based estimation of Krylov subspace dimension and Padé order.•High computational efficiency.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114844