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Certificates of positivity for real polynomials : theory, practice, and applications / Victoria Powers.
Powers, Victoria, author.
2021
QA161.P59 P68 2021
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Title
Certificates of positivity for real polynomials : theory, practice, and applications / Victoria Powers.
Author
Powers, Victoria, author.
ISBN
9783030855475 (electronic bk.)
3030855473 (electronic bk.)
9783030855468
3030855465
DOI
https://doi.org/10.1007/978-3-030-85547-5
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations
Item Number
10.1007/978-3-030-85547-5 doi
Call Number
QA161.P59 P68 2021
Dewey Decimal Classification
512.9/422
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 2, 2021).
Series
Developments in mathematics ; v. 69. 2197-795X
Available in Other Form
Certificates of positivity for real polynomials.
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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.

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