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Interpolation Of Rational Matrix Functions
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Book Synopsis Interpolation of Rational Matrix Functions by : Joseph Ball
Download or read book Interpolation of Rational Matrix Functions written by Joseph Ball and published by Birkhäuser. This book was released on 2013-11-11 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).
Book Synopsis Topics in Interpolation Theory of Rational Matrix-valued Functions by : I. Gohberg
Download or read book Topics in Interpolation Theory of Rational Matrix-valued Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2013-11-21 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the basic interpolation problems from our point of view is the problem of building a scalar rational function if its poles and zeros with their multiplicities are given. If one assurnes that the function does not have a pole or a zero at infinity, the formula which solves this problem is (1) where Zl , " " Z/ are the given zeros with given multiplicates nl, " " n / and Wb" " W are the given p poles with given multiplicities ml, . . . ,m , and a is an arbitrary nonzero number. p An obvious necessary and sufficient condition for solvability of this simplest Interpolation pr- lern is that Zj :f: wk(1~ j ~ 1, 1~ k~ p) and nl +. . . +n/ = ml +. . . +m ' p The second problem of interpolation in which we are interested is to build a rational matrix function via its zeros which on the imaginary line has modulus 1. In the case the function is scalar, the formula which solves this problem is a Blaschke product, namely z z. )mi n u(z) = all = l~ (2) J ( Z+ Zj where [o] = 1, and the zj's are the given zeros with given multiplicities mj. Here the necessary and sufficient condition for existence of such u(z) is that zp :f: - Zq for 1~ ]1, q~ n.
Book Synopsis Topics in Interpolation Theory of Rational Matrix-valued Functions by : Israel Gohberg
Download or read book Topics in Interpolation Theory of Rational Matrix-valued Functions written by Israel Gohberg and published by . This book was released on 1988 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Extension and Interpolation of Linear Operators and Matrix Functions by : I. Gohberg
Download or read book Extension and Interpolation of Linear Operators and Matrix Functions written by I. Gohberg and published by Birkhäuser. This book was released on 2013-11-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation by : Harry Dym
Download or read book $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation written by Harry Dym and published by American Mathematical Soc.. This book was released on 1989 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.
Book Synopsis Analysis and Partial Differential Equations by : Cora Sadosky
Download or read book Analysis and Partial Differential Equations written by Cora Sadosky and published by CRC Press. This book was released on 1989-12-15 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a descriptive account of Mischa Cotlar's work along with a complete bibliography of his mathematical books and papers. It examines the harmonic analysis and operator theory in relation with the theory of partial differential equations.
Book Synopsis Orthogonal Rational Functions by : Adhemar Bultheel
Download or read book Orthogonal Rational Functions written by Adhemar Bultheel and published by Cambridge University Press. This book was released on 1999-02-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book generalises the classical theory of orthogonal polynomials to rational functions.
Book Synopsis Matrix Theory and Applications by : Charles R. Johnson
Download or read book Matrix Theory and Applications written by Charles R. Johnson and published by American Mathematical Soc.. This book was released on 1990 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on Operator Theory and Its Applications by : Albrecht Böttcher
Download or read book Lectures on Operator Theory and Its Applications written by Albrecht Böttcher and published by American Mathematical Soc.. This book was released on with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures presented at a meeting on operator theory and its applications held at the Fields Insitute in 1994.
Book Synopsis Linear Algebra for Control Theory by : Paul Van Dooren
Download or read book Linear Algebra for Control Theory written by Paul Van Dooren and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a natural outflow of this research, this book presents information on this interdisciplinary area. The cross-fertilization between control and linear algebra can be found in subfields such as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control. This book's editors were challenged to present the latest results in these areas and to find points of common interest. This volume reflects very nicely the interaction: the range of topics seems very wide indeed, but the basic problems and techniques are always closely connected. And the common denominator in all of this is, of course, linear algebra. This book is suitable for both mathematicians and students.
Book Synopsis Operator Theory and Complex Analysis by : J. K. Aggarwal
Download or read book Operator Theory and Complex Analysis written by J. K. Aggarwal and published by Springer Science & Business Media. This book was released on 1993-01-22 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a set of papers based on the proceedings of the NATO Advanced Research Workshop on Multisensor Fusion for Computer Vision, held in Grenoble, France, in June 1989. The workshop focused on the fusion or integration of sensor information to achieve the optimum interpretation of a scene. The papers cover a broad range of topics, including principles and issues in multisensor fusion, information fusion for navigation, multisensor fusion for object recognition, network approaches to multisensor fusion, computer architectures for multisensor fusion, and applications of multisensor fusion. The authors have documented their own research and, in so doing,have presented the state of the art in the field. Each author is a recognized leader in his or her area in the academic, governmental, or industrial research community. Several contributors present novel points of view on the integration of information. The book gives a representative picture of current progress in multisensor fusion for computer vision among the leading research groups in Europe and North America.
Book Synopsis Operator Theory and Complex Analysis by : T. Ando
Download or read book Operator Theory and Complex Analysis written by T. Ando and published by Birkhäuser. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Matrix and Operator Theory by : H. Bart
Download or read book Topics in Matrix and Operator Theory written by H. Bart and published by Birkhäuser. This book was released on 2013-11-22 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Signal Processing and Systems Theory by : Charles K. Chui
Download or read book Signal Processing and Systems Theory written by Charles K. Chui and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Signal Processing and Systems Theory" is concerned with the study of H-optimization for digital signal processing and discrete-time control systems. The first three chapters present the basic theory and standard methods in digital filtering and systems from the frequency-domain approach, followed by a discussion of the general theory of approximation in Hardy spaces. AAK theory is introduced, first for finite-rank operators and then more generally, before being extended to the multi-input/multi-output setting. This mathematically rigorous book is self-contained and suitable for self-study. The advanced mathematical results derived here are applicable to digital control systems and digital filtering.
Book Synopsis Interpolation, Schur Functions and Moment Problems II by : Daniel Alpay
Download or read book Interpolation, Schur Functions and Moment Problems II written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.
Book Synopsis The Schur Algorithm, Reproducing Kernel Spaces and System Theory by : Daniel Alpay
Download or read book The Schur Algorithm, Reproducing Kernel Spaces and System Theory written by Daniel Alpay and published by American Mathematical Soc.. This book was released on 2001 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of Schur functions consists of analytic functions on the unit disk that are bounded by $1$. The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering. In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Societe Mathematique de France. Translated by Stephen S. Wilson.
Book Synopsis Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations by : Daniel Alpay
Download or read book Operator Theory, Systems Theory and Scattering Theory: Multidimensional Generalizations written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
