Noncommutative Plurisubharmonic Polynomials PDF Download
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Author | : Jeremy Michael Greene |
Publisher | : |
Total Pages | : 67 |
Release | : 2011 |
Genre | : |
ISBN | : 9781124670843 |
Download Noncommutative Plurisubharmonic Polynomials Book in PDF, ePub and Kindle
Many optimization problems and engineering problems connected with linear systems lead to matrix inequalities. Matrix inequalities are constraints in which a polynomial or a matrix of polynomials with matrix variables is required to take a positive semidefinite value. Many of these problems have the property that they are "dimension free" and, in this case, the form of the polynomials remains the same for matrices of all size. In other words, we have noncommutative polynomials. One very much desires these polynomials to be "convex" in the unknown matrix variables, since if they are, then numerical calculations are reliable and local optima are global optima. In this dissertation, we classify all changes of variables (not containing transposes) from noncommutative non-convex polynomials to noncommutative convex polynomials. This introduces notions of noncommutative complex Hessians and plurisubharmonicity, classical notions from several complex variables. In addition, we present a theory of noncommutative integration and we prove a "local implies global" result in that we show noncommutative plurisubharmonicity on a noncommutative open set implies noncommutative plurisubharmonicity everywhere.
Author | : Grigoriy Blekherman |
Publisher | : SIAM |
Total Pages | : 487 |
Release | : 2013-03-21 |
Genre | : Mathematics |
ISBN | : 1611972280 |
Download Semidefinite Optimization and Convex Algebraic Geometry Book in PDF, ePub and Kindle
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Author | : Christopher Scott Nelson |
Publisher | : |
Total Pages | : 88 |
Release | : 2012 |
Genre | : |
ISBN | : 9781267607898 |
Download Non-commutative Harmonic and Subharmonic Polynomials and Other Non-commutative Partial Differential Equations Book in PDF, ePub and Kindle
Author | : Sabine Burgdorf |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2016-07-16 |
Genre | : Mathematics |
ISBN | : 9783319333366 |
Download Optimization of Polynomials in Non-Commuting Variables Book in PDF, ePub and Kindle
This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
Author | : HUISHI. LI |
Publisher | : Chapman & Hall/CRC Monographs and Research Notes in Mathematics |
Total Pages | : 232 |
Release | : 2021-11-08 |
Genre | : |
ISBN | : 9781032079882 |
Download Noncommutative Polynomial Algebras of Solvable Type and Their Modules Book in PDF, ePub and Kindle
This is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. This book is perfectly suited to researchers and postgrads researching noncommutative computational algebra.
Author | : Jeremy Judah Stone |
Publisher | : |
Total Pages | : 90 |
Release | : 1960 |
Genre | : Algebraic functions |
ISBN | : |
Download Exponential Polynomials on Commutative Semigroups Book in PDF, ePub and Kindle
Author | : Victor V. Prasolov |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2004-07-09 |
Genre | : Mathematics |
ISBN | : 9783540407140 |
Download Polynomials Book in PDF, ePub and Kindle
Covers its topic in greater depth than the typical standard books on polynomial algebra
Author | : Francisco Marcellàn |
Publisher | : Springer |
Total Pages | : 432 |
Release | : 2006-10-18 |
Genre | : Mathematics |
ISBN | : 3540367160 |
Download Orthogonal Polynomials and Special Functions Book in PDF, ePub and Kindle
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.
Author | : Renato Alvarez-Nodarse |
Publisher | : Nova Publishers |
Total Pages | : 222 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9781594540097 |
Download Laredo Lectures on Orthogonal Polynomials and Special Functions Book in PDF, ePub and Kindle
This new book presents research in orthogonal polynomials and special functions. Recent developments in the theory and accomplishments of the last decade are pointed out and directions for research in the future are identified. The topics covered include matrix orthogonal polynomials, spectral theory and special functions, Asymptotics for orthogonal polynomials via Riemann-Hilbert methods, Polynomial wavelets and Koornwinder polynomials.
Author | : A. Schinzel |
Publisher | : Cambridge University Press |
Total Pages | : 590 |
Release | : 2000-04-27 |
Genre | : Mathematics |
ISBN | : 9781139426718 |
Download Polynomials with Special Regard to Reducibility Book in PDF, ePub and Kindle
This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Results valid only over finite fields, local fields or the rational field are not covered here, but several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields are included. Some of these results are based on recent work of E. Bombieri and U. Zannier (presented here by Zannier in an appendix). The book also treats other subjects like Ritt's theory of composition of polynomials, and properties of the Mahler measure, and it concludes with a bibliography of over 300 items. This unique work will be a necessary resource for all number theorists and researchers in related fields.