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Titlebook: Interpolation of Rational Matrix Functions; Joseph A. Ball,Israel Gohberg,Leiba Rodman Book 1990 Springer Basel AG 1990 constraint.control

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书目名称Interpolation of Rational Matrix Functions
编辑Joseph A. Ball,Israel Gohberg,Leiba Rodman
视频video
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Interpolation of Rational Matrix Functions;  Joseph A. Ball,Israel Gohberg,Leiba Rodman Book 1990 Springer Basel AG 1990 constraint.control
描述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 meth
出版日期Book 1990
关键词constraint; control; equation; functions; Interpolation; Mathematica; Meromorphic function; model; Nevanlinn
版次1
doihttps://doi.org/10.1007/978-3-0348-7709-1
isbn_softcover978-3-0348-7711-4
isbn_ebook978-3-0348-7709-1Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightSpringer Basel AG 1990
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Null Structure and Interpolation Problems for Matrix Polynomialsout also that .(.) is regular, i.e. det .(.) does not vanish identically. One of our aims is to specify for matrix polynomials in a detailed way the theory developed in the first chapter for analytic matrix functions. We also solve here the first interpolation problem in this book, namely, how to co
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Rational Matrix Functionslation problem, namely to build a rational matrix function with a given null and pole structure. Unlike the scalar case, it turns out that even when the solution exists and the value at infinity is specified, it may not be unique. A particular solution can be singled out if additional information is
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Rational Matrix Functions with Null and Pole Structure at Infinity requires a more general realization theory and allows one to solve less restrictive interpolation problems of constructing a rational matrix function with a given null and pole structure. The special case of matrix polynomials, which may be considered as rational matrix functions with only pole at
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Rational Matrix Functions with ,-Unitary Values on the Unit Circle the case .-unitary values on the unit circle. The developments here parallel those in Chapter 6 for the case of the imaginary axis. The treatment of the null and pole structure at infinity is given additional attention. As in Chapter 6, also here . is a fixed . × . signature matrix.
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Interpolation Problems for Rational Matrix Functions Based on Divisibilityshould serve as divisors of the function to be determined. We assume that the poles and zeros of the given divisors are in disjoint regions .., ..,...,.. of the complex plane, and we require that the interpolant . should have the property that for each . the quotient .. should have no zeros or poles
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