Positive Polynomials and Sums of Squares

Positive Polynomials and Sums of Squares
Author :
Publisher : American Mathematical Soc.
Total Pages : 201
Release :
ISBN-10 : 9780821844021
ISBN-13 : 0821844024
Rating : 4/5 (024 Downloads)

Book Synopsis Positive Polynomials and Sums of Squares by : Murray Marshall

Download or read book Positive Polynomials and Sums of Squares written by Murray Marshall and published by American Mathematical Soc.. This book was released on 2008 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures. This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. The focus is on the exciting new developments that have taken place in the last 15 years, arising out of Schmudgen's solution to the moment problem in the compact case in 1991. The book is accessible to a well-motivated student at the beginning graduate level. The objects being dealt with are concrete and down-to-earth, namely polynomials in $n$ variables with real coefficients, and many examples are included. Proofs are presented as clearly and as simply as possible. Various new, simpler proofs appear in the book for the first time. Abstraction is employed only when it serves a useful purpose, but, at the same time, enough abstraction is included to allow the reader easy access to the literature. The book should be essential reading for any beginning student in the area.


Positive Polynomials and Sums of Squares Related Books

Positive Polynomials and Sums of Squares
Language: en
Pages: 201
Authors: Murray Marshall
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry when study
Positive Polynomials in Control
Language: en
Pages: 332
Authors: Didier Henrion
Categories: Technology & Engineering
Type: BOOK - Published: 2005-01-14 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Positive Polynomials in Control originates from an invited session presented at the IEEE CDC 2003 and gives a comprehensive overview of existing results in this
Moments, Positive Polynomials and Their Applications
Language: en
Pages: 384
Authors: Jean-Bernard Lasserre
Categories: Mathematics
Type: BOOK - Published: 2010 - Publisher: World Scientific

DOWNLOAD EBOOK

1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -
Positive Polynomials
Language: en
Pages: 269
Authors: Alexander Prestel
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.).
Positive Trigonometric Polynomials and Signal Processing Applications
Language: en
Pages: 282
Authors: Bogdan Dumitrescu
Categories: Technology & Engineering
Type: BOOK - Published: 2017-03-20 - Publisher: Springer

DOWNLOAD EBOOK

This book gathers the main recent results on positive trigonometric polynomials within a unitary framework. The book has two parts: theory and applications. The