Material Type  

 단행본

Date and Time of Latest Transaction  

20121210094821

ISBN  

9781400840595 (electronic bk.)

ISBN  

1400840597 (electronic bk.)

ISBN  

9780691128894

ISBN  

0691128898

LC Callnumber  

QA188-.B35 2011eb

DDC  

512.9434-23

Author  

Bakonyi, M.((Mihály)) , 1962-

Title/Author  

Matrix completions, moments, and sums of hermitian squares - [electronic resource] : Mihály Bakonyi and Hugo J. Woerdeman

Publish Info  

Princeton : Princeton University Press, c2011

Material Info  

1 online resource (xii, 518 p) : ill.

총서명  

Princeton series in applied mathematics

서지주기  

Includes bibliographical references (p. [475]-512) and indexes.

Formatted Contents Note  

완전내용Cover -- Contents -- Preface -- Chapter 1. Cones of Hermitian matrices and trigonometric polynomials -- 1.1 Cones and their basic properties -- 1.2 Cones of Hermitian matrices -- 1.3 Cones of trigonometric polynomials -- 1.4 Determinant and entropy maximization -- 1.5 Semidefinite programming -- 1.6 Exercises -- 1.7 Notes -- Chapter 2. Completions of positive semidefinite operator matrices -- 2.1 Positive definite completions: the banded case -- 2.2 Positive definite completions: the chordal case -- 2.3 Positive definite completions: the Toeplitz case -- 2.4 The Schur complement and Fej233;r-Riesz factorization -- 2.5 Schur parameters -- 2.6 The central completion, maximum entropy, and inheritance principle -- 2.7 The Hamburger moment problem and spectral factorization on the real line -- 2.8 Linear prediction -- 2.9 Exercises -- 2.10 Notes -- Chapter 3. Multivariable moments and sums of Hermitian squares -- 3.1 Positive Carath233;odory interpolation on the polydisk -- 3.2 Inverses of multivariable Toeplitz matrices and Christoffel-Darboux formulas -- 3.3 Two-variable moment problem for Bernstein-Szeg246; measures -- 3.4 Fej233;r-Riesz factorization and sums of Hermitian squares -- 3.5 Completion problems for positive semidefinite functions on amenable groups -- 3.6 Moment problems on free groups -- 3.7 Noncommutative factorization -- 3.8 Two-variable Hamburger moment problem -- 3.9 Bochners theorem and an application to autoregressive stochastic processes -- 3.10 Exercises -- 3.11 Notes -- Chapter 4. Contractive analogs -- 4.1 Contractive operator-matrix completions -- 4.2 Linearly constrained completion problems -- 4.3 The operator-valued Nehari and Carath233;odory problems -- 4.4 Neharis problem in two variables -- 4.5 Nehari and Carath233;odory problems for functions on compact groups -- 4.6 The Nevanlinna-Pick problem -- 4.7 The operator Corona problem -- 4.8 Joint operator/Hilbert-Schmidt norm control extensions -- 4.9 An L[sup()] extension problem for polynomials -- 4.10 Superoptimal completions -- 4.11 Superoptimal approximations of analytic functions -- 4.12 Model matching -- 4.13 Exercises -- 4.14 Notes -- Chapter 5. Hermitian and related completion problems -- 5.1 Hermitian completions -- 5.2 Ranks of completions -- 5.3 Minimal negative and positive signature -- 5.4 Inertia of Hermitian matrix expressions -- 5.5 Bounds for eigenvalues of Hermitian completions -- 5.6 Bounds for singular values of completions of partial triangular matrices -- 5.7 Moment problems for real measures on the unit circle -- 5.8 Euclidean distance matrix completions -- 5.9 Normal completions -- 5.10 Application to minimal representation of discrete systems -- 5.11 The separability problem in quantum information -- 5.12 Exercises -- 5.13 Notes -- Bibliography -- Subject Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Notation Index.

Abstracts/Etc  

요약Intensive 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.

Subject Added Entry-Topical Term  

Algebras, Linear

Subject Added Entry-Topical Term  

Hermitian forms

Subject Added Entry-Topical Term  

Matrices

Subject Added Entry-Topical Term  

MATHEMATICS Matrices.

Added Entry-Personal Name  

Woerdeman, Hugo J.((Hugo Jan)) , 1962-

Additional Physical Form Entry  

Print versionBakonyi, M. (Mihály), 1962- Matrix Completions, moments, and sums of Hermitian squares. Princeton, N.J. ; Oxford : Princeton UP, c2011 9780691128894 0691128898 (OCoLC)724663096

Series Added Entry-Uniform Title  

Princeton series in applied mathematics.

Electronic Location and Access  

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Control Number  

joongbu:397092