| 书目名称 | Certificates of Positivity for Real Polynomials | | 副标题 | Theory, Practice, an | | 编辑 | Victoria Powers | | 视频video | | | 概述 | Includes extensive background information for increased accessibility.Contains discussion of computational and algorithmic aspects of the subject.Features an extensive bibliography | | 丛书名称 | Developments in Mathematics | | 图书封面 |  | | 描述 | .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 19.th. 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 | | 出版日期 | Book 2021 | | 关键词 | semialgebraic sets and related spaces; sums of squares; ternary quartics; Polya‘s theorem; Scheiderer‘s | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-85547-5 | | isbn_softcover | 978-3-030-85549-9 | | isbn_ebook | 978-3-030-85547-5Series ISSN 1389-2177 Series E-ISSN 2197-795X | | issn_series | 1389-2177 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 17:09:00
