Concentrated matrix exponential distributions

Illés Horváth, Orsolya Sáfár, M. Telek, Bence Zámbó

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (cv). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the cv cannot be less than 0.200902 but the proof of this conjecture is still missing. In previous literature ME distributions with low cv are obtained from special subclasses of ME distributions (for odd and even orders), which are conjectured to contain the ME distribution with minimal cv. The numerical search for the extreme distribution in the special ME subclasses is easier for odd orders and previously computed for orders up to 15. The numerical treatment of the special subclass of the even orders is much harder and extreme distribution had been found only for order 4. In this work, we further extend the numerical optimization for subclasses of odd orders (up to order 47), and also for subclasses of even order (up to order 14). We also determine the parameters of the extreme distributions, and compare the properties of the optimal ME distributions for odd and even order. Finally, based on the numerical results we draw conclusions on both, the behavior of the odd and the even orders.

Original languageEnglish
Title of host publicationComputer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings
PublisherSpringer Verlag
Pages18-31
Number of pages14
Volume9951 LNCS
ISBN (Print)9783319464329
DOIs
Publication statusPublished - 2016
Event13th European Workshop on Computer Performance Engineering, EPEW 2016 - Chios, Greece
Duration: Oct 5 2016Oct 7 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9951 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th European Workshop on Computer Performance Engineering, EPEW 2016
CountryGreece
CityChios
Period10/5/1610/7/16

Fingerprint

Matrix Exponential
Exponential distribution
Coefficient of variation
Odd
Extremes
Numerical Optimization

Keywords

  • Matrix exponential distributions
  • Minimal coefficient of variation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Horváth, I., Sáfár, O., Telek, M., & Zámbó, B. (2016). Concentrated matrix exponential distributions. In Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings (Vol. 9951 LNCS, pp. 18-31). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9951 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-46433-6_2

Concentrated matrix exponential distributions. / Horváth, Illés; Sáfár, Orsolya; Telek, M.; Zámbó, Bence.

Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings. Vol. 9951 LNCS Springer Verlag, 2016. p. 18-31 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9951 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Horváth, I, Sáfár, O, Telek, M & Zámbó, B 2016, Concentrated matrix exponential distributions. in Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings. vol. 9951 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9951 LNCS, Springer Verlag, pp. 18-31, 13th European Workshop on Computer Performance Engineering, EPEW 2016, Chios, Greece, 10/5/16. https://doi.org/10.1007/978-3-319-46433-6_2
Horváth I, Sáfár O, Telek M, Zámbó B. Concentrated matrix exponential distributions. In Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings. Vol. 9951 LNCS. Springer Verlag. 2016. p. 18-31. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-46433-6_2
Horváth, Illés ; Sáfár, Orsolya ; Telek, M. ; Zámbó, Bence. / Concentrated matrix exponential distributions. Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings. Vol. 9951 LNCS Springer Verlag, 2016. pp. 18-31 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{0ab98dbf9136434e9860780bacbe0e70,
title = "Concentrated matrix exponential distributions",
abstract = "We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (cv). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the cv cannot be less than 0.200902 but the proof of this conjecture is still missing. In previous literature ME distributions with low cv are obtained from special subclasses of ME distributions (for odd and even orders), which are conjectured to contain the ME distribution with minimal cv. The numerical search for the extreme distribution in the special ME subclasses is easier for odd orders and previously computed for orders up to 15. The numerical treatment of the special subclass of the even orders is much harder and extreme distribution had been found only for order 4. In this work, we further extend the numerical optimization for subclasses of odd orders (up to order 47), and also for subclasses of even order (up to order 14). We also determine the parameters of the extreme distributions, and compare the properties of the optimal ME distributions for odd and even order. Finally, based on the numerical results we draw conclusions on both, the behavior of the odd and the even orders.",
keywords = "Matrix exponential distributions, Minimal coefficient of variation",
author = "Ill{\'e}s Horv{\'a}th and Orsolya S{\'a}f{\'a}r and M. Telek and Bence Z{\'a}mb{\'o}",
year = "2016",
doi = "10.1007/978-3-319-46433-6_2",
language = "English",
isbn = "9783319464329",
volume = "9951 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "18--31",
booktitle = "Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings",

}

TY - GEN

T1 - Concentrated matrix exponential distributions

AU - Horváth, Illés

AU - Sáfár, Orsolya

AU - Telek, M.

AU - Zámbó, Bence

PY - 2016

Y1 - 2016

N2 - We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (cv). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the cv cannot be less than 0.200902 but the proof of this conjecture is still missing. In previous literature ME distributions with low cv are obtained from special subclasses of ME distributions (for odd and even orders), which are conjectured to contain the ME distribution with minimal cv. The numerical search for the extreme distribution in the special ME subclasses is easier for odd orders and previously computed for orders up to 15. The numerical treatment of the special subclass of the even orders is much harder and extreme distribution had been found only for order 4. In this work, we further extend the numerical optimization for subclasses of odd orders (up to order 47), and also for subclasses of even order (up to order 14). We also determine the parameters of the extreme distributions, and compare the properties of the optimal ME distributions for odd and even order. Finally, based on the numerical results we draw conclusions on both, the behavior of the odd and the even orders.

AB - We revisit earlier attempts for finding matrix exponential (ME) distributions of a given order with low coefficient of variation (cv). While there is a long standing conjecture that for the first non-trivial order, which is order 3, the cv cannot be less than 0.200902 but the proof of this conjecture is still missing. In previous literature ME distributions with low cv are obtained from special subclasses of ME distributions (for odd and even orders), which are conjectured to contain the ME distribution with minimal cv. The numerical search for the extreme distribution in the special ME subclasses is easier for odd orders and previously computed for orders up to 15. The numerical treatment of the special subclass of the even orders is much harder and extreme distribution had been found only for order 4. In this work, we further extend the numerical optimization for subclasses of odd orders (up to order 47), and also for subclasses of even order (up to order 14). We also determine the parameters of the extreme distributions, and compare the properties of the optimal ME distributions for odd and even order. Finally, based on the numerical results we draw conclusions on both, the behavior of the odd and the even orders.

KW - Matrix exponential distributions

KW - Minimal coefficient of variation

UR - http://www.scopus.com/inward/record.url?scp=84989962335&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989962335&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46433-6_2

DO - 10.1007/978-3-319-46433-6_2

M3 - Conference contribution

SN - 9783319464329

VL - 9951 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 18

EP - 31

BT - Computer Performance Engineering - 13th European Workshop, EPEW 2016, Proceedings

PB - Springer Verlag

ER -