From Polynomials To Sums Of Squares

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From Polynomials To Sums Of Squares

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Author : T.H Jackson
language : en
Publisher: CRC Press
Release Date : 2023-05-09

From Polynomials To Sums Of Squares written by T.H Jackson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Mathematics categories.

From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer.

From Polynomials To Sums Of Squares

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Author : Terence Hugh Jackson
language : en
Publisher:
Release Date : 2020

From Polynomials To Sums Of Squares written by Terence Hugh Jackson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with MATHEMATICS categories.

From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer.

Positive Polynomials And Sums Of Squares

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Author : Murray Marshall
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Positive Polynomials And Sums Of Squares written by Murray Marshall and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

The study of positive polynomials brings together algebra, geometry and analysis. The subject is of fundamental importance in real algebraic geometry when studying the properties of objects defined by polynomial inequalities. Hilbert's 17th problem and its solution in the first half of the 20th century were landmarks in the early days of the subject. More recently, new connections to the moment problem and to polynomial optimization have been discovered. The moment problem relates linear maps on the multidimensional polynomial ring to positive Borel measures. This book provides an elementary introduction to positive polynomials and sums of squares, the relationship to the moment problem, and the application to polynomial optimization. The focus is on the exciting new developments that have taken place in the last 15 years, arising out of Schmudgen's solution to the moment problem in the compact case in 1991. The book is accessible to a well-motivated student at the beginning graduate level. The objects being dealt with are concrete and down-to-earth, namely polynomials in $n$ variables with real coefficients, and many examples are included. Proofs are presented as clearly and as simply as possible. Various new, simpler proofs appear in the book for the first time. Abstraction is employed only when it serves a useful purpose, but, at the same time, enough abstraction is included to allow the reader easy access to the literature. The book should be essential reading for any beginning student in the area.

Sum Of Squares Theory And Applications

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Author : Pablo A. Parrilo
language : en
Publisher: American Mathematical Soc.
Release Date :

Sum Of Squares Theory And Applications written by Pablo A. Parrilo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Education categories.

This volume is based on lectures delivered at the 2019 AMS Short Course “Sum of Squares: Theory and Applications”, held January 14–15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science. The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.

Nonnegative Polynomials And Sums Of Squares

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Author : Sadik Iliman
language : en
Publisher:
Release Date : 2014

Nonnegative Polynomials And Sums Of Squares written by Sadik Iliman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

Sums Of Squares Of Polynomials In R X1 X Subscript N

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Author : Colin Starr
language : en
Publisher:
Release Date : 1998

Sums Of Squares Of Polynomials In R X1 X Subscript N written by Colin Starr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Positive Polynomials Sums Of Squares And The Moment Problem

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Author : Tim Netzer
language : en
Publisher:
Release Date : 2008

Positive Polynomials Sums Of Squares And The Moment Problem written by Tim Netzer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Polynomials

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Author : Victor V. Prasolov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-23

Polynomials written by Victor V. Prasolov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-23 with Mathematics categories.

Covers its topic in greater depth than the typical standard books on polynomial algebra

Bounded Polynomials Sums Of Squares And The Moment Problem

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Author : Daniel Plaumann
language : en
Publisher:
Release Date : 2008

Bounded Polynomials Sums Of Squares And The Moment Problem written by Daniel Plaumann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Nonnegative Polynomials Sums Of Squares And The Cayley Bacharach Theorem

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Author : Kenneth T. Henderson
language : en
Publisher:
Release Date : 2016

Nonnegative Polynomials Sums Of Squares And The Cayley Bacharach Theorem written by Kenneth T. Henderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

It is a difficult problem to prove that a polynomial only takes non-negative values. One way to certify that a polynomial is non-negative is to express it as a sum of squares, however not all non-negative polynomials can be written as a sum of squares. The fundamental reason that there exist non-negative polynomials that cannot be written as sums of squares is that these polynomials satisfy linear inequalities that arise from linear relations known as the Cayley-Bacharach relations. Using the smallest cases where there exist such non-negative polynomials as motivating problems, we explore the history of the Cayley-Bacharach theorem from which these relations arise. The exploration of the development of this theorem, beginning with Pappus of Alexandria and ending in modern terms, reflects the changing motivation of the field of algebraic geometry. Along with the history of the theorem we provide the necessary background for the techniques used in proving each statement.