Activity of order n in continuous systems
In this work we generalize the concept of activity of continuous time signals. We define the activity of order n of a signal and show that it allows us to estimate the number of sections of polynomials up to order n which are needed to represent that signal with a certain accuracy. Then we apply thi...
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2015
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00375497_v91_n4_p337_Castro http://hdl.handle.net/20.500.12110/paper_00375497_v91_n4_p337_Castro |
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paper:paper_00375497_v91_n4_p337_Castro2023-06-08T15:02:19Z Activity of order n in continuous systems Activity tracking continuous systems discrete event simulation numerical solvers quantized state systems Discrete event simulation Activity tracking Continuous system Continuous-time signal Integration algorithm Integration method Lower bounds Numerical solvers Quantized state systems Continuous time systems In this work we generalize the concept of activity of continuous time signals. We define the activity of order n of a signal and show that it allows us to estimate the number of sections of polynomials up to order n which are needed to represent that signal with a certain accuracy. Then we apply this concept to obtain a lower bound for the number of steps performed by quantization-based integration algorithms in the simulation of ordinary differential equations. We perform an exhaustive analysis over two examples, computing the activity of order n and comparing it with the number of steps performed by different integration methods. This analysis corroborates the theoretical predictions and also allows us to measure the suitability of the different algorithms depending on how close to the theoretical lower bound they perform. © 2015, The Author(s). All rights reserved. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00375497_v91_n4_p337_Castro http://hdl.handle.net/20.500.12110/paper_00375497_v91_n4_p337_Castro |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Activity tracking continuous systems discrete event simulation numerical solvers quantized state systems Discrete event simulation Activity tracking Continuous system Continuous-time signal Integration algorithm Integration method Lower bounds Numerical solvers Quantized state systems Continuous time systems |
| spellingShingle |
Activity tracking continuous systems discrete event simulation numerical solvers quantized state systems Discrete event simulation Activity tracking Continuous system Continuous-time signal Integration algorithm Integration method Lower bounds Numerical solvers Quantized state systems Continuous time systems Activity of order n in continuous systems |
| topic_facet |
Activity tracking continuous systems discrete event simulation numerical solvers quantized state systems Discrete event simulation Activity tracking Continuous system Continuous-time signal Integration algorithm Integration method Lower bounds Numerical solvers Quantized state systems Continuous time systems |
| description |
In this work we generalize the concept of activity of continuous time signals. We define the activity of order n of a signal and show that it allows us to estimate the number of sections of polynomials up to order n which are needed to represent that signal with a certain accuracy. Then we apply this concept to obtain a lower bound for the number of steps performed by quantization-based integration algorithms in the simulation of ordinary differential equations. We perform an exhaustive analysis over two examples, computing the activity of order n and comparing it with the number of steps performed by different integration methods. This analysis corroborates the theoretical predictions and also allows us to measure the suitability of the different algorithms depending on how close to the theoretical lower bound they perform. © 2015, The Author(s). All rights reserved. |
| title |
Activity of order n in continuous systems |
| title_short |
Activity of order n in continuous systems |
| title_full |
Activity of order n in continuous systems |
| title_fullStr |
Activity of order n in continuous systems |
| title_full_unstemmed |
Activity of order n in continuous systems |
| title_sort |
activity of order n in continuous systems |
| publishDate |
2015 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00375497_v91_n4_p337_Castro http://hdl.handle.net/20.500.12110/paper_00375497_v91_n4_p337_Castro |
| _version_ |
1768544542785536000 |