On the measure of polynomials attaining maxima on a vertex

Autores
Pinasco, Damian; Zalduendo, Ignacio Martin
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of dimension and degree. We find that the behavior of vertices with orthogonal edges is markedly different to that of sharper vertices. If the degree k grows with the dimension n, the probability that a polynomial attain a local maximum tends to 1/2, but for orthogonal edges the growth-rate of k must be larger than nlnn, while for sharper vertices a growth-rate larger than lnn will suffice.
Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; Argentina
Materia
POLYNOMIAL, MEASURE OF POLYNOMIALS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/118446
Acceder
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spelling On the measure of polynomials attaining maxima on a vertexPinasco, DamianZalduendo, Ignacio MartinPOLYNOMIAL, MEASURE OF POLYNOMIALShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of dimension and degree. We find that the behavior of vertices with orthogonal edges is markedly different to that of sharper vertices. If the degree k grows with the dimension n, the probability that a polynomial attain a local maximum tends to 1/2, but for orthogonal edges the growth-rate of k must be larger than nlnn, while for sharper vertices a growth-rate larger than lnn will suffice.Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; ArgentinaElement2019-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/118446Pinasco, Damian; Zalduendo, Ignacio Martin; On the measure of polynomials attaining maxima on a vertex; Element; Mathematical Inequalities & Applications; 22; 2; 3-2019; 421-4321331-4343CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://mia.ele-math.com/22-30/On-the-measure-of-polynomials-attaining-maxima-on-a-vertexinfo:eu-repo/semantics/altIdentifier/doi/10.7153/mia-2019-22-30info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:28:50Zoai:ri.conicet.gov.ar:11336/118446instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:28:50.651CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the measure of polynomials attaining maxima on a vertex
title On the measure of polynomials attaining maxima on a vertex
spellingShingle On the measure of polynomials attaining maxima on a vertex
Pinasco, Damian
POLYNOMIAL, MEASURE OF POLYNOMIALS
title_short On the measure of polynomials attaining maxima on a vertex
title_full On the measure of polynomials attaining maxima on a vertex
title_fullStr On the measure of polynomials attaining maxima on a vertex
title_full_unstemmed On the measure of polynomials attaining maxima on a vertex
title_sort On the measure of polynomials attaining maxima on a vertex
dc.creator.none.fl_str_mv Pinasco, Damian
Zalduendo, Ignacio Martin
author Pinasco, Damian
author_facet Pinasco, Damian
Zalduendo, Ignacio Martin
author_role author
author2 Zalduendo, Ignacio Martin
author2_role author
dc.subject.none.fl_str_mv POLYNOMIAL, MEASURE OF POLYNOMIALS
topic POLYNOMIAL, MEASURE OF POLYNOMIALS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of dimension and degree. We find that the behavior of vertices with orthogonal edges is markedly different to that of sharper vertices. If the degree k grows with the dimension n, the probability that a polynomial attain a local maximum tends to 1/2, but for orthogonal edges the growth-rate of k must be larger than nlnn, while for sharper vertices a growth-rate larger than lnn will suffice.
Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Zalduendo, Ignacio Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella; Argentina
description We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of dimension and degree. We find that the behavior of vertices with orthogonal edges is markedly different to that of sharper vertices. If the degree k grows with the dimension n, the probability that a polynomial attain a local maximum tends to 1/2, but for orthogonal edges the growth-rate of k must be larger than nlnn, while for sharper vertices a growth-rate larger than lnn will suffice.
publishDate 2019
dc.date.none.fl_str_mv 2019-03
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/118446
Pinasco, Damian; Zalduendo, Ignacio Martin; On the measure of polynomials attaining maxima on a vertex; Element; Mathematical Inequalities & Applications; 22; 2; 3-2019; 421-432
1331-4343
CONICET Digital
CONICET
url http://hdl.handle.net/11336/118446
identifier_str_mv Pinasco, Damian; Zalduendo, Ignacio Martin; On the measure of polynomials attaining maxima on a vertex; Element; Mathematical Inequalities & Applications; 22; 2; 3-2019; 421-432
1331-4343
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://mia.ele-math.com/22-30/On-the-measure-of-polynomials-attaining-maxima-on-a-vertex
info:eu-repo/semantics/altIdentifier/doi/10.7153/mia-2019-22-30
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Element
publisher.none.fl_str_mv Element
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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