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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/118446
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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 Técnicas2025-09-29T09:59:28Zoai: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:34982025-09-29 09:59:29.209CONICET 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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1844613764573298688 |
score |
13.070432 |