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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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 421; S. 114844 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier B.V
15.03.2023
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 114844 |
| Author | Jimenez, J.C. Naranjo-Noda, F.S. |
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| Cites_doi | 10.1016/j.cam.2016.09.013 10.1137/S0036142995280572 10.1016/j.jcp.2020.109946 10.1007/s10543-011-0332-6 10.1109/TAC.1978.1101743 10.1137/1020098 10.1016/j.aml.2015.04.009 10.1016/j.jcp.2005.08.032 10.1016/S0167-6911(02)00150-0 10.1093/imamci/dnaa021 10.1007/s10543-011-0360-2 10.1137/040607356 10.1145/2168773.2168781 10.1145/285861.285868 10.1093/imamci/dnx047 10.1137/0729014 10.1016/j.cam.2007.01.007 |
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| References | Jimenez, de la Cruz (b8) 2012; 52 Jimenez, Mora, Selva (b20) 2017; 313 Carbonell, Jimenez, Pedroso (b2) 2008; 213 Van Loan (b1) 1978; AC-23 Maybeck (b5) 1982 Tokman (b11) 2006; 213 Jimenez (b22) 2020; 37 Crassidis, Junkins (b3) 2004 de la Cruz, Biscay, Carbonell, Ozaki, Jimenez (b16) 2007; 185 Moler, Van Loan (b14) 1978; 20 Jimenez, Pedroso, Carbonell, Hernadez (b15) 2006; 44 Hochbruck, Lubich (b6) 1997; 34 Hochbruck, Ostermann (b17) 2011; 51 Naranjo-Noda, Jimenez (b10) 2021; 426 Sidje (b7) 1998; 24 Jimenez (b21) 2019; 36 Grewal, Andrews (b4) 2014 Jimenez (b19) 2015; 49 Niesen, Wright (b9) 2012; 38 Golub, Van Loan (b13) 1996 Saad (b12) 1992; 29 Jimenez, Ozaki (b18) 2002; 47 Hochbruck (10.1016/j.cam.2022.114844_b6) 1997; 34 Jimenez (10.1016/j.cam.2022.114844_b15) 2006; 44 Jimenez (10.1016/j.cam.2022.114844_b22) 2020; 37 Tokman (10.1016/j.cam.2022.114844_b11) 2006; 213 Carbonell (10.1016/j.cam.2022.114844_b2) 2008; 213 Jimenez (10.1016/j.cam.2022.114844_b19) 2015; 49 Maybeck (10.1016/j.cam.2022.114844_b5) 1982 Moler (10.1016/j.cam.2022.114844_b14) 1978; 20 Jimenez (10.1016/j.cam.2022.114844_b21) 2019; 36 Jimenez (10.1016/j.cam.2022.114844_b20) 2017; 313 Crassidis (10.1016/j.cam.2022.114844_b3) 2004 Niesen (10.1016/j.cam.2022.114844_b9) 2012; 38 Jimenez (10.1016/j.cam.2022.114844_b18) 2002; 47 Grewal (10.1016/j.cam.2022.114844_b4) 2014 Hochbruck (10.1016/j.cam.2022.114844_b17) 2011; 51 Van Loan (10.1016/j.cam.2022.114844_b1) 1978; AC-23 Jimenez (10.1016/j.cam.2022.114844_b8) 2012; 52 Sidje (10.1016/j.cam.2022.114844_b7) 1998; 24 Naranjo-Noda (10.1016/j.cam.2022.114844_b10) 2021; 426 de la Cruz (10.1016/j.cam.2022.114844_b16) 2007; 185 Saad (10.1016/j.cam.2022.114844_b12) 1992; 29 Golub (10.1016/j.cam.2022.114844_b13) 1996 |
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