Lanczos-Like Algorithm for the Time-Ordered Exponential: The *-Inverse Problem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422775" target="_blank" >RIV/00216208:11320/20:10422775 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1QY5SvrCLH" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1QY5SvrCLH</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2020.0342-19" target="_blank" >10.21136/AM.2020.0342-19</a>
Alternative languages
Result language
angličtina
Original language name
Lanczos-Like Algorithm for the Time-Ordered Exponential: The *-Inverse Problem
Original language description
The time-ordered exponential of a time-dependent matrix A(t) is defined as the function of A(t) that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in A(t). The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by *. Yet, the existence of such inverses, crucial to avoid algorithmic breakdowns, still needed to be proved. Here we constructively prove that *-inverses exist for all non-identically null, smooth, separable functions of two variables. As a corollary, we partially solve the Green's function inverse problem which, given a distribution G, asks for the differential operator whose fundamental solution is G. Our results are abundantly illustrated by examples.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
1572-9109
Volume of the periodical
65
Issue of the periodical within the volume
6
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
21
Pages from-to
807-827
UT code for WoS article
000575698200001
EID of the result in the Scopus database
2-s2.0-85092100915