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MARC 21

Certificates of Positivity for Real Polynomials: Theory, Practice, and Applications /
Tag	Description
020	$a9783030855475$9978-3-030-85547-5
082	$a516.35$223
099	$aOnline resource: Springer
100	$aPowers, Victoria.$eauthor.$4aut$4http://id.loc.gov/vocabulary/relators/aut
245	$aCertificates of Positivity for Real Polynomials$h[EBook] :$bTheory, Practice, and Applications /$cby Victoria Powers.
250	$a1st ed. 2021.
260	$aCham :$bSpringer International Publishing :$bImprint: Springer,$c2021.
300	$aXI, 156 p. 14 illus.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aDevelopments in Mathematics,$x2197-795X ;$v69
505	$a1. 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.
520	$aThis 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.
533	$nMode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
830	$aDevelopments in Mathematics,$x2197-795X ;$v69
856	$uhttps://doi.org/10.1007/978-3-030-85547-5