Meromorphic Functions and Linear Algebra
Language: English
Published by American Mathematical Society, US, 2003
- Hardcover
- New
Seller: Rarewaves.com UK, London, United KingdomRarewaves.com UK
AbeBooks seller since June 11, 2025
Condition: New
£ 54.46
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Add to basketItem description from seller
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
- Title
- Meromorphic Functions and Linear Algebra
- Author
- Olavi Nevanlinna
- Publisher
- American Mathematical Society, US
- Publication year
- 2003
- Condition
- New
- Binding
- Hardback
- Language
- English
- ISBN 10
- 0821832476
- ISBN 13
- 9780821832479
- Item weight
- 510 grams
- Dimensions
- 17.78 x 1.27 x 25.4 cm
"Synopsis" may belong to another edition of this title.
Rarewaves.com UK
London, United Kingdom
AbeBooks seller since June 11, 2025
Shipping rates from United Kingdom to U.S.A.
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