Synopsis
This monograph proposes that viewing the resolvent of a matrix as a meromorphic function rather than just analytic outside the eigenvalues provides new insight, and develops a new non-linear tool for linear algebra the total logarithmic size of a matrix which allows the author to generalization his uncle's first main theorem from the scalar valued case for matrix valued functions. The author then proves the robustness of the growth of the resolvent as a meromorphic function under low rank perturbations, and studies the growth of a meromorphic function by approximating rational functions. Annotation (c) Book News, Inc., Portland, OR (booknews.com)
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Meromorphic Functions and Linear Algebra (eng)
Published by
Amer Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Meromorphic Functions and Linear Algebra
Published by
American Mathematical Society, US, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Hardback. Condition: New. This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essentially unchanged. This has practical implications to the analysis of iterative solvers for large systems of linear algebraic equations.First, the book introduces the basics of value distribution theory of meromorphic scalar functions. It then introduces a new nonlinear tool for linear algebra, the total logarithmic size of a matrix, which allows for a nontrivial generalization of Rolf Nevanlinna's characteristic function from the scalar theory to matrix- and operator-valued functions. In particular, the theory of perturbations by low rank matrices becomes possible. As an example, if the spectrum of a normal matrix collapses under a low rank perturbation, there is always a compensation in terms of the loss of orthogonality of the eigenvectors.This qualitative phenomenon is made quantitative by using the new tool. Applications are given to rational approximation, to the Kreiss matrix theorem, and to convergence of Krylov solvers. The book is intended for researchers in mathematics in general and especially for those working in numerical linear algebra. Much of the book is understandable if the reader has a good background in linear algebra and a first course in complex analysis. Seller Inventory # LU-9780821832479
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Meromorphic Functions and Linear Algebra
Published by
Amer Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Meromorphic Functions and Linear Algebra (Fields Institute Monographs, 18)
Published by
Amer Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Hardcover. Condition: Brand New. 136 pages. 10.00x7.00x0.50 inches. In Stock. Seller Inventory # __0821832476
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Meromorphic Functions and Linear Algebra
Published by
Amer Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Meromorphic Functions and Linear Algebra
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American Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Condition: New. Describes in monograph form important applications in numerical methods of linear algebra. This book studies the behavior of the resolvent of a matrix under the perturbation by low rank matrices. It also introduces the basics of value distribution theory of meromorphic scalar functions. Series: Fields Institute Monographs. Num Pages: 136 pages. BIC Classification: PBF; PBKD; PBKS. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 263 x 182 x 13. Weight in Grams: 484. . 2003. Y First Edition. hardcover. . . . . Seller Inventory # V9780821832479
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Meromorphic Functions and Linear Algebra
Published by
American Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Meromorphic Functions and Linear Algebra
Published by
American Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Seller: Kennys Bookstore, Olney, MD, U.S.A.
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Condition: New. Describes in monograph form important applications in numerical methods of linear algebra. This book studies the behavior of the resolvent of a matrix under the perturbation by low rank matrices. It also introduces the basics of value distribution theory of meromorphic scalar functions. Series: Fields Institute Monographs. Num Pages: 136 pages. BIC Classification: PBF; PBKD; PBKS. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 263 x 182 x 13. Weight in Grams: 484. . 2003. Y First Edition. hardcover. . . . . Books ship from the US and Ireland. Seller Inventory # V9780821832479
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Meromorphic Functions and Linear Algebra
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MP-AMM American Mathematical, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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Meromorphic Functions and Linear Algebra
Published by
American Mathematical Society, 2003
ISBN 10: 0821832476
ISBN 13: 9780821832479
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