Overview
- Includes extensive background information for increased accessibility
- Contains discussion of computational and algorithmic aspects of the subject
- Features an extensive bibliography
Part of the book series: Developments in Mathematics (DEVM, volume 69)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positivity for a real polynomial is an algebraic identity that gives an immediate proof of a positivity condition for the polynomial. Certificates of positivity have their roots in fundamental work of David Hilbert from the late 19th century on positive polynomials and sums of squares. Because of the numerous applications of certificates of positivity in mathematics, applied mathematics, engineering, and other fields, it is desirable to have methods for finding, describing, and characterizing them. For many of the topics covered in this book, appropriate algorithms, computational methods, and applications are discussed.
This volume contains a comprehensive, accessible, up-to-date treatment of certificates of positivity, written by an expert in the field. It provides an overview of both the theory and computational aspects of the subject, and includes many of the recent and exciting developments in the area. Background information is given so that beginning graduate students and researchers who are not specialists can learn about this fascinating subject. Furthermore, researchers who work on certificates of positivity or use them in applications will find this a useful reference for their work.
Reviews
“The book under review is a very nice introduction to the central topic of real algebra … . The book is very well written with many examples demonstrating the statements of the main results. … In the reviewer's opinion this is a very nice and concise presentation of the most important pillars of real algebra up to the present time.” (Aljaž Zalar, Mathematical Reviews, June, 2023)
“This book introduces several theories with applications ... . Also, the book includes introductions to various recent developments ... . The author described the results as friendly as possible with sufficient intuitions and examples. ... This book provides a good introduction to certificates of positivity who want to learn this area as a beginner.” (Jaewoo Jung, zbMATH 1483.14001, 2022)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Certificates of Positivity for Real Polynomials
Book Subtitle: Theory, Practice, and Applications
Authors: Victoria Powers
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-030-85547-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-85546-8Published: 26 November 2021
Softcover ISBN: 978-3-030-85549-9Published: 27 November 2022
eBook ISBN: 978-3-030-85547-5Published: 26 November 2021
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XI, 156
Number of Illustrations: 14 b/w illustrations
Topics: Algebraic Geometry, Number Theory, Computer Science, general