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Meromorphic functions and linear algebra

Author: Olavi Nevanlinna
Publisher: Providence, R.I. : American Mathematical Society, ©2003.
Series: Fields Institute monographs, 18.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"Some results appear here for the first time, while the rest are extended from recent papers of the author. 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."--Jacket.
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Olavi Nevanlinna
ISBN: 0821832476 9780821832479
OCLC Number: 51241993
Description: x, 136 pages ; 27 cm.
Contents: Tapping away in an evening at Djursholm --
What does an epsilon weigh? --
Red wine at the Stock Exchange Club --
Ice-cream in Madison --
Exact equality --
The deficiency of values --
Zurich --
Beautiful to look at, but ... --
The unbearable ease of using norms --
Centenary Colloquium in Joensuu --
Two basic tasks, stability first --
And then accelerating the iteration --
Factoring the resolvent --
In the Hermann Weyl lecture hall --
A quiet life in Warsaw --
Finally, in Kirkkonummi --
Resolvent --
Cauchy-integral --
Entire functions --
Taylor coefficients --
Meromorphic functions --
The first main theorem --
Cartan's identity --
Order and type for meromorphic functions --
Boutroux-Cartan lemma --
Bound along a circle --
Representation theorems --
Analytic vector valued functions --
Subharmonic functions --
Meromorphic vector valued functions --
Rational functions --
When is the inverse also meromorphic --
A simple estimate for matrices --
A product form for matrices --
Singular value decomposition --
Basic inequalities for singular values and eigenvalues --
The total logarithmic size of a matrix --
Some basic properties of the total logarithmic size --
Direct sum, Kronecker product and Hadamard product --
The total logarithmic size is subharmonic --
Behavior near poles --
Introducing T[subscript 1] for matrix valued functions --
Basic identity for inversion --
Extension to trace class --
How to work outside the trace class --
Perturbation results --
Special results for resolvents --
Powers and their resolvents.
Series Title: Fields Institute monographs, 18.
Responsibility: Olavi Nevanlinna.

Abstract:

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  Read more...

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