Recent advances in matrix and operator theory

Joseph A. Ball, Joseph A. Ball, Yuli Eidelman, J. William Helton, Vadim Olshevsky, James Rovnyak9783764385385, 3764385383

This book expands the lectures given at IWOTA 05 (International Workshop on Operator Theory and Applications) which was held at the University of Connecticut, Storrs, USA, July 24 27, 2005. Many developments on the cutting edge of research in operator theory, matrix theory, coding theory, system theory, control theory and numerical linear algebra are reflected in this collection of original articles.

The volume is of a cross-disciplinary nature. A number of papers are devoted to the analysis and algorithms for matrices with quasiseparable structure which is an active area of concurrent research in numerical linear algebra.

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Table of contents :
Editorial Introduction……Page 7
Contents……Page 5
Inverse Problems for First-Order DiscreteSystems……Page 8
Stability of Dynamical Systems via SemidefiniteProgramming……Page 32
Ranks of Hadamard Matrices andEquivalence of Sylvester–Hadamard andPseudo-Noise Matrices……Page 42
Image of a Jacobi Field……Page 54
The Higher Order Carath´eodory–JuliaTheorem and Related BoundaryInterpolation Problems……Page 70
A Generalization to Ordered Groupsof a Kreın Theorem……Page 110
A Fast QR Algorithm for Companion Matrices……Page 117
The Numerical Range of a Class ofSelf-adjoint Operator Functions……Page 150
A Perturbative Analysis of the Reductioninto Diagonal-plus-semiseparable Form ofSymmetric Matrices……Page 161
The Eigenstructure of Complex SymmetricOperators……Page 172
Higher Order Asymptotic Formulasfor Traces of Toeplitz Matrices withSymbols in H¨older-Zygmund Spaces……Page 187
On an Eigenvalue Problem for Some NonlinearTransformations of Multi-dimensional Arrays……Page 199
On Embedding of the Bratteli Diagraminto a Surface……Page 213
Superfast Inversion of Two-Level ToeplitzMatrices Using Newton Iteration andTensor-Displacement Structure……Page 230
On Generalized Numerical Rangesof Quadratic Operators……Page 242
Inverse Problems for Canonical DifferentialEquations with Singularities……Page 258
On Triangular Factorization of PositiveOperators……Page 290
Solutions for the H∞(Dn) Corona ProblemBelonging to exp(L12n−1)……Page 310
A Matrix and its Inverse: Revisiting MinimalRank Completions……Page 330