Treffer: Approximating sums of squares with a single square
Title:
Approximating sums of squares with a single square
Authors:
Source:
Special Issue devoted to papers presented at the International Meeting on Matrix Analysis and Applications, Ft. Lauderdale, FL, 14-16 December 2003Linear algebra and its applications. 399:187-201
Publisher Information:
New York, NY: Elsevier Science, 2005.
Publication Year:
2005
Physical Description:
print, 16 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Factorisation spectrale, Spectral factorization, Factorización espectral, Fonction n variables, N variable function, Función n variables, Groupe Lie, Lie group, Grupo Lie, Polynôme trigonométrique, Trigonometric polynomial, Polinomio trigonométrico, Programmation semi définie, Semi definite programming, Programacíon semi definida, Tore, Torus, Toro, 15A48, 42B05, 93B36 Spectral factorization, Multivariable trigonometric polynomial, Outer component, Semidetinite programming, Sums of squares
Document Type:
Konferenz
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Electrabel, Regentlaan/Bd du Régent 8, 1000 Brussels, Belgium
Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, United States
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium
Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, United States
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Heverlee, Belgium
ISSN:
0024-3795
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.16667917
Database:
PASCAL Archive
Weitere Informationen
In this paper, we explore the following question. Given a trigonometric polynomial q(z1, zd) of several variables that is non-negative on the d-torus, how does one best approximate q with a (possibly outer) single modulus square? Our answer will lie in the notion of an outer component, which coincides with the outer factor in the case of one variable. The outer component may be computed numerically using semidefinite programming. We shall derive some properties of outer components, as well as pose some open problems.