Certificates of Positivity for Real Polyno...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Zusammenfassung

Includes extensive background information for increased accessibility

Contains discussion of computational and algorithmic aspects of the subject

Features an extensive bibliography

Inhaltsverzeichnis

1. Preliminaries.- 2. Sums of Squares and Positive Polynomials. - 3. Global Certificates of Positivity.- 4. Positive Semidefinite Ternary Quartics.- 5. Positivity on Semialgebraic Sets.- 6. The Archimedean Property.- 7. Theorems of Schmudgen and Putinar.- 8. The Dimension One Case.- 9. Positivity on Polytopes.- 10. The Noncompact Case.- 11. Sums of Squares of Rational Polynomials.- 12. Positive Polynomials with Special Structure.- Real Algebra and Algebraic Geometry.- Index of Notation.- Index.

Details

Erscheinungsjahr:	2022
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xi 156 S. 14 s/w Illustr. 156 p. 14 illus.
ISBN-13:	9783030855499
ISBN-10:	303085549X
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Powers, Victoria
Auflage:	1st edition 2021
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 10 mm
Von/Mit:	Victoria Powers
Erscheinungsdatum:	27.11.2022
Gewicht:	0,265 kg

Artikel-ID: 125797056