Interpolation By Rational Matrix Functions With Minimal Mcmillan Degree
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Interpolation Of Rational Matrix Functions
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Author : Joseph Ball
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Interpolation Of Rational Matrix Functions written by Joseph Ball and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Social Science categories.
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).
Interpolation By Rational Matrix Functions With Minimal Mcmillan Degree
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Author : Jeongook Kim Kang
language : en
Publisher:
Release Date : 1990
Interpolation By Rational Matrix Functions With Minimal Mcmillan Degree written by Jeongook Kim Kang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Interpolation categories.
Topics In Interpolation Theory Of Rational Matrix Valued Functions
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Author : I. Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2013-11-21
Topics In Interpolation Theory Of Rational Matrix Valued Functions written by I. Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Social Science categories.
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.
Interpolation And Realization Theory With Applications To Control Theory
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Author : Vladimir Bolotnikov
language : en
Publisher: Springer
Release Date : 2019-04-08
Interpolation And Realization Theory With Applications To Control Theory written by Vladimir Bolotnikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-08 with Mathematics categories.
This volume is devoted to Joseph A. (Joe) Ball’s contributions to operator theory and its applications and in celebration of his seventieth birthday. Joe Ball’s career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions and operators on multiply connected domains. Later on, more applied operator theory themes appeared in his work, involving factorization and interpolation for operator-valued functions, with extensive applications in system and control theory. He has worked on nonlinear control, time-varying systems and, more recently, on multidimensional systems and noncommutative H∞-theory on the unit ball and polydisk, and more general domains, and these are only the main themes in his vast oeuvre. Fourteen research papers constitute the core of this volume, written by mathematicians who have collaborated with Joe or have been influenced by his vast mathematical work. A curriculum vitae, a publicationslist and a list of Joe Ball’s PhD students are included in this volume, as well as personal reminiscences by colleagues and friends. Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S. Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J. Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton.
Extension And Interpolation Of Linear Operators And Matrix Functions
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Author : I. Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Extension And Interpolation Of Linear Operators And Matrix Functions written by I. Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
New Aspects In Interpolation And Completion Theories
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Author : I. Gohberg
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
New Aspects In Interpolation And Completion Theories written by I. Gohberg and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
This volume consists of eight papers containing recent advances in interpolation theory for matrix functions and completion theory for matrices and operators. In the first paper, D. Alpay and P. Loubaton, "The tangential trigonometric moment problem on an interval and related topics" a trigonometric moment problem on an interval for matrix valued functions is studied. The realization approach plays an important role in solving this problem. The second paper, M. Bakonyi, V.G. Kaftal, G. Weiss and H.J. Woerdeman, "Max imum entropy and joint norm bounds for operator extensions" is dedicated to a matrix completion problem. In it is considered the problem when only the lower triangular part of the operator entries of a matrix is identified. Completions which have simultaneously a small usual norm and a small Hilbert-Schmidt norm are considered. Bounds for these norms are obtained. The analysis of the maximum entropy extension plays a special role. The paper contains applications to nest algebras and integral operators. The third paper, J .A. Ball, I. Gohberg and M.A. Kaashoek, "Bitangential interpola tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems. The main attention is focused on the time varying analog of the Nevanlinna-Pick tangential problem in the case where the inter polation conditions appear from two sides. The state space theory of time varying systems play an important role.
Linear Algebra For Control Theory
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Author : Paul Van Dooren
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebra For Control Theory written by Paul Van Dooren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Interpolation Schur Functions And Moment Problems
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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-22
Interpolation Schur Functions And Moment Problems written by Daniel Alpay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-22 with Mathematics categories.
Schur analysis originated with an 1917 article which associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients, often named reflection coefficients in signal processing. This volume comprises seven essays dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
Operator Theory And Complex Analysis
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Author : T. Ando
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Theory And Complex Analysis written by T. Ando and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
Operator Theory And Complex Analysis
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Author : J. K. Aggarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-01-22
Operator Theory And Complex Analysis written by J. K. Aggarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-22 with Computers categories.
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.