A note on integrating products of linear forms over the unit simplex

Fuente: arXiv
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Autor principal: Casale, Giuliano
Formato: Preprint
Publicado: 2017
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author Casale, Giuliano
author_facet Casale, Giuliano
contents Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the normalizing constant of state probabilities for a popular class of Markov processes used in queueing network theory. In light of this equivalence, we survey existing computational algorithms developed in queueing theory that can be used for exact integration. For example, under some regularity conditions, queueing theory algorithms can exactly integrate a product of linear forms of total degree N by solving N systems of linear equations.
format Preprint
id arxiv_https___arxiv_org_abs_1704_05867
institution arXiv
publishDate 2017
record_format arxiv
spellingShingle A note on integrating products of linear forms over the unit simplex
Casale, Giuliano
Performance
Metric Geometry
C.4; G.2
Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the normalizing constant of state probabilities for a popular class of Markov processes used in queueing network theory. In light of this equivalence, we survey existing computational algorithms developed in queueing theory that can be used for exact integration. For example, under some regularity conditions, queueing theory algorithms can exactly integrate a product of linear forms of total degree N by solving N systems of linear equations.
title A note on integrating products of linear forms over the unit simplex
topic Performance
Metric Geometry
C.4; G.2
url https://arxiv.org/abs/1704.05867