Sum Of Squares Theory And Applications
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Sum Of Squares Theory And Applications
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Author : Pablo A. Parrilo
language : en
Publisher: American Mathematical Soc.
Release Date : 2020
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 2020 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.
Sums Of Squares Of Integers
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Author : Carlos J. Moreno
language : en
Publisher: CRC Press
Release Date : 2005-12-09
Sums Of Squares Of Integers written by Carlos J. Moreno and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-09 with Mathematics categories.
Sums of Squares of Integers covers topics in combinatorial number theory as they relate to counting representations of integers as sums of a certain number of squares. The book introduces a stimulating area of number theory where research continues to proliferate. It is a book of "firsts" - namely it is the first book to combine Liouville's elementary methods with the analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares of integers for any s and n. It is also the first book to give a proof of Szemeredi's theorem, and is the first number theory book to discuss how the modern theory of modular forms complements and clarifies the classical fundamental results about sums of squares. The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
Positive Trigonometric Polynomials And Signal Processing Applications
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Author : Bogdan Dumitrescu
language : en
Publisher: Springer
Release Date : 2018-07-21
Positive Trigonometric Polynomials And Signal Processing Applications written by Bogdan Dumitrescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-21 with Technology & Engineering categories.
This book gathers the main recent results on positive trigonometric polynomials within a unitary framework. The book has two parts: theory and applications. The theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The applications part is organized as a collection of related problems that use systematically the theoretical results.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Commutative Ring Theory And Applications
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Author : Marco Fontana
language : en
Publisher: CRC Press
Release Date : 2017-07-27
Commutative Ring Theory And Applications written by Marco Fontana and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-27 with Mathematics categories.
Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome
Theory And Application Of Special Functions
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Author : Richard Askey
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Theory And Application Of Special Functions written by Richard Askey and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.
Latin Squares And Their Applications
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Author : A. Donald Keedwell
language : en
Publisher: Elsevier
Release Date : 2015-07-28
Latin Squares And Their Applications written by A. Donald Keedwell and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-28 with Mathematics categories.
Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader 'from the beginnings of the subject to the frontiers of research'. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties. - Retains the organization and updated foundational material from the original edition - Explores current and emerging research topics - Includes the original 73 'Unsolved Problems' with the current state of knowledge regarding them, as well as new Unsolved Problems for further study
From Polynomials To Sums Of Squares
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Author : T.H Jackson
language : en
Publisher: CRC Press
Release Date : 1995-01-01
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 1995-01-01 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.
The Total Least Squares Problem
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Author : Sabine Van Huffel
language : en
Publisher: SIAM
Release Date : 1991-01-01
The Total Least Squares Problem written by Sabine Van Huffel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
Image Recovery Theory And Application
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Author : Henry Stark
language : en
Publisher: Elsevier
Release Date : 2013-04-25
Image Recovery Theory And Application written by Henry Stark and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-25 with Technology & Engineering categories.
Image Recovery: Theory and Application focuses on signal recovery and synthesis problems. This book discusses the concepts of image recovery, including regularization, the projection theorem, and the pseudoinverse operator. Comprised of 13 chapters, this volume begins with a review of the basic properties of linear vector spaces and associated operators, followed by a discussion on the Gerchberg-Papoulis algorithm. It then explores image restoration and the basic mathematical theory in image restoration problems. The reader is also introduced to the problem of obtaining artifact-free computed tomographic reconstruction. Other chapters consider the importance of Bayesian approach in the context of medical imaging. In addition, the book discusses the linear programming method, which is particularly important for images with large number of pixels with zero value. Such images are usually found in medical imaging, microscopy, electron microscopy, and astronomy. This book can be a valuable resource to materials scientists, engineers, computed tomography technologists, and astronomers.