The Real Positive Definite Completion Problem

Author : Wayne Walton Barrett,Charles R. Johnson,Raphael Loewy
Publisher : American Mathematical Soc.
Page : 69 pages
File Size : 51,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804735

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The Real Positive Definite Completion Problem by Wayne Walton Barrett,Charles R. Johnson,Raphael Loewy Pdf

Given a partial symmetric matrix, the positive definite completion problem asks if the unspecified entries in the matrix can be chosen so as to make the resulting matrix positive definite. Applications include probability and statistics, image enhancement, systems engineering, geophysics, and mathematical programming. The positive definite completion problem can also be viewed as a mechanism for addressing a fundamental problem in Euclidean geometry: which potential geometric configurations of vectors (i.e., configurations with angles between some vectors specified) are realizable in a Euclidean space. The positions of the specified entries in a partial matrix are naturally described by a graph. The question of existence of a positive definite completion was previously solved completely for the restrictive class of chordal graphs and this work solves the problem for the class of cycle completable graphs, a significant generalization of chordal graphs. These are the graphs for which knowledge of completability for induced cycles (and cliques) implies completability of partial symmetric matrices with the given graph.

Author : Dragana S. Cvetković Ilić
Publisher : American Mathematical Society
Page : 170 pages
File Size : 51,8 Mb
Release : 2022-06-07
Category : Mathematics
ISBN : 9781470469870

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Completion Problems on Operator Matrices by Dragana S. Cvetković Ilić Pdf

Completion problems for operator matrices are concerned with the question of whether a partially specified operator matrix can be completed to form an operator of a desired type. The research devoted to this topic provides an excellent means to investigate the structure of operators. This book provides an overview of completion problems dealing with completions to different types of operators and can be considered as a natural extension of classical results concerned with matrix completions. The book assumes some basic familiarity with functional analysis and operator theory. It will be useful for graduate students and researchers interested in operator theory and the problem of matrix completions.

Author : Wayne Walton Barrett
Publisher : Unknown
Page : 69 pages
File Size : 46,5 Mb
Release : 1996
Category : Graph theory
ISBN : 147040169X

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The Real Positive Definite Completion Problem by Wayne Walton Barrett Pdf

Author : Panos M. Pardalos and Henry Wolkowicz
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 54,6 Mb
Release : 2024-05-23
Category : Interior-point methods
ISBN : 0821871250

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Topics in Semidefinite and Interior-Point Methods by Panos M. Pardalos and Henry Wolkowicz Pdf

This volume presents refereed papers presented at the workshop Semidefinite Programming and Interior-Point Approaches for Combinatorial Problems: held at The Fields Institute in May 1996. Semidefinite programming (SDP) is a generalization of linear programming (LP) in that the non-negativity constraints on the variables is replaced by a positive semidefinite constraint on matrix variables. Many of the elegant theoretical properties and powerful solution techniques follow through from LP to SDP. In particular, the primal-dual interior-point methods, which are currently so successful for LP, can be used to efficiently solve SDP problems. In addition to the theoretical and algorithmic questions, SDP has found many important applications in combinatorial optimization, control theory and other areas of mathematical programming. The papers in this volume cover a wide spectrum of recent developments in SDP. The volume would be suitable as a textbook for advanced courses in optimization. It is intended for graduate students and researchers in mathematics, computer science, engineering and operations.

Author : Mihály Bakonyi,Hugo J. Woerdeman
Publisher : Princeton University Press
Page : 533 pages
File Size : 47,7 Mb
Release : 2011-07-18
Category : Mathematics
ISBN : 9781400840595

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Matrix Completions, Moments, and Sums of Hermitian Squares by Mihály Bakonyi,Hugo J. Woerdeman Pdf

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.

Author : Naomi Shaked-monderer,Abraham Berman
Publisher : World Scientific
Page : 562 pages
File Size : 42,8 Mb
Release : 2021-02-09
Category : Mathematics
ISBN : 9789811204364

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Copositive And Completely Positive Matrices by Naomi Shaked-monderer,Abraham Berman Pdf

This book is an updated and extended version of Completely Positive Matrices (Abraham Berman and Naomi Shaked-Monderer, World Scientific 2003). It contains new sections on the cone of copositive matrices, which is the dual of the cone of completely positive matrices, and new results on both copositive matrices and completely positive matrices.The book is an up to date comprehensive resource for researchers in Matrix Theory and Optimization. It can also serve as a textbook for an advanced undergraduate or graduate course.

Author : Harm Bart,Sanne ter Horst,André C.M. Ran,Hugo J. Woerdeman
Publisher : Springer
Page : 464 pages
File Size : 49,9 Mb
Release : 2018-12-30
Category : Mathematics
ISBN : 9783030042691

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Operator Theory, Analysis and the State Space Approach by Harm Bart,Sanne ter Horst,André C.M. Ran,Hugo J. Woerdeman Pdf

This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of Rien Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J. Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S. Malysheva, A. Böttcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B. Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J. Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S. Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 49,6 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Author : Charles R. Johnson
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 45,8 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821801543

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Matrix Theory and Applications by Charles R. Johnson Pdf

This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

Author : Anonim
Publisher : Unknown
Page : 960 pages
File Size : 47,7 Mb
Release : 2007
Category : Mathematics
ISBN : UCSD:31822036024826

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SIAM Journal on Matrix Analysis and Applications by Anonim Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1402 pages
File Size : 44,7 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 9781420010572

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Handbook of Linear Algebra by Leslie Hogben Pdf

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl

Author : Károly Bezdek,Antoine Deza,Yinyu Ye
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 40,5 Mb
Release : 2013-07-09
Category : Mathematics
ISBN : 9783319002002

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Discrete Geometry and Optimization by Károly Bezdek,Antoine Deza,Yinyu Ye Pdf

​Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems.

Author : Marloes Maathuis,Mathias Drton,Steffen Lauritzen,Martin Wainwright
Publisher : CRC Press
Page : 536 pages
File Size : 50,9 Mb
Release : 2018-11-12
Category : Mathematics
ISBN : 9780429874246

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Handbook of Graphical Models by Marloes Maathuis,Mathias Drton,Steffen Lauritzen,Martin Wainwright Pdf

A graphical model is a statistical model that is represented by a graph. The factorization properties underlying graphical models facilitate tractable computation with multivariate distributions, making the models a valuable tool with a plethora of applications. Furthermore, directed graphical models allow intuitive causal interpretations and have become a cornerstone for causal inference. While there exist a number of excellent books on graphical models, the field has grown so much that individual authors can hardly cover its entire scope. Moreover, the field is interdisciplinary by nature. Through chapters by leading researchers from different areas, this handbook provides a broad and accessible overview of the state of the art. Key features: * Contributions by leading researchers from a range of disciplines * Structured in five parts, covering foundations, computational aspects, statistical inference, causal inference, and applications * Balanced coverage of concepts, theory, methods, examples, and applications * Chapters can be read mostly independently, while cross-references highlight connections The handbook is targeted at a wide audience, including graduate students, applied researchers, and experts in graphical models.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1906 pages
File Size : 46,9 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781466507289

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Handbook of Linear Algebra, Second Edition by Leslie Hogben Pdf

With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.