Geometric Product for Multidimensional Dynamical Systems - Laplace Transform and Geometric Algebra

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43957978" target="_blank" >RIV/49777513:23520/18:43957978 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1109/EECS.2018.00018" target="_blank" >http://dx.doi.org/10.1109/EECS.2018.00018</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/EECS.2018.00018" target="_blank" >10.1109/EECS.2018.00018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Geometric Product for Multidimensional Dynamical Systems - Laplace Transform and Geometric Algebra

Popis výsledku v původním jazyce

This contribution describes a new approach to a solution of multidimensional dynamical systems using the Laplace transform and geometrical product, i.e. using inner product (dot product, scalar product) and outer product (extended cross-product). It leads to a linear system of equations Ax=0 or Ax=b which is equivalent to the outer product if the projective extension of the Euclidean system and the principle of duality are used. The paper explores property of the geometrical product in the frame of multidimensional dynamical systems. The proposed approach enables to avoid division operation and extents numerical precision as well. It also offers applications of matrix-vector and vector-vector operations in symbolic manipulation, which can lead to new algorithms and/or new formula. The proposed approach can be applied also for stability evaluation of dynamical systems. In the case of numerical computation, it supports vector operation and SSE instructions or GPU can be used efficiently.

Název v anglickém jazyce

Geometric Product for Multidimensional Dynamical Systems - Laplace Transform and Geometric Algebra

Popis výsledku anglicky

This contribution describes a new approach to a solution of multidimensional dynamical systems using the Laplace transform and geometrical product, i.e. using inner product (dot product, scalar product) and outer product (extended cross-product). It leads to a linear system of equations Ax=0 or Ax=b which is equivalent to the outer product if the projective extension of the Euclidean system and the principle of duality are used. The paper explores property of the geometrical product in the frame of multidimensional dynamical systems. The proposed approach enables to avoid division operation and extents numerical precision as well. It also offers applications of matrix-vector and vector-vector operations in symbolic manipulation, which can lead to new algorithms and/or new formula. The proposed approach can be applied also for stability evaluation of dynamical systems. In the case of numerical computation, it supports vector operation and SSE instructions or GPU can be used efficiently.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA17-05534S" target="_blank" >GA17-05534S: Meshless metody pro vizualizaci velkých časově-prostorových vektorových dat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název statě ve sborníku

2018 2nd European Conference on Electrical Engineering and Computer Science (EECS)

ISBN

978-1-72811-929-8

ISSN

—

e-ISSN

—

Počet stran výsledku

5

Strana od-do

45-49

Název nakladatele

IEEE

Místo vydání

Piscataway

Místo konání akce

Bern

Datum konání akce

20. 12. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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