Lanczos-Like Algorithm for the Time-Ordered Exponential: The *-Inverse Problem

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Lanczos-Like Algorithm for the Time-Ordered Exponential: The *-Inverse Problem

Popis výsledku v původním jazyce

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&apos;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.

Název v anglickém jazyce

Lanczos-Like Algorithm for the Time-Ordered Exponential: The *-Inverse Problem

Popis výsledku anglicky

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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

1572-9109

Svazek periodika

65

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

21

Strana od-do

807-827

Kód UT WoS článku

000575698200001

EID výsledku v databázi Scopus

2-s2.0-85092100915