Numerical Range
The Field of Values of Linear Operators and Matrices
(Sprache: Englisch)
This book is dedicated to presenting the fundamentals of numerical ranges. In order to make it quickly informative the authors place and keep the subject in a complex Hilbert space. This setting is the heart of the numerical range theory for bounded linear...
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Klappentext zu „Numerical Range “
This book is dedicated to presenting the fundamentals of numerical ranges. In order to make it quickly informative the authors place and keep the subject in a complex Hilbert space. This setting is the heart of the numerical range theory for bounded linear operators T. This text is a particularly well prepared account of a beautiful and interesting part of functional analysis which appears to have important applications in numerical analysis.
Inhaltsverzeichnis zu „Numerical Range “
1 Numerical Range.- 1.1 Elliptic Range.- 1.2 Spectral Inclusion.- 1.3 Numerical Radius.- 1.4 Normal Operators.- 1.5 Numerical Boundary.- 1.6 Other W-Ranges.- Endnotes for Chapter 1.- 2 Mapping Theorems.- 2.1 Radius Mapping.- 2.2 Analytic Functions.- 2.3 Rational Functions.- 2.4 Operator Products.- 2.5 Commuting Operators.- 2.6 Dilation Theory.- Endnotes for Chapter 2.- 3 Operator Trigonometry.- 3.1 Operator Angles.- 3.2 Minmax Equality.- 3.3 Operator Deviations.- 3.4 Semigroup Generators.- 3.5 Accretive Products.- 3.6 Antieigenvalue Theory.- Endnotes for Chapter 3.- 4 Numerical Analysis.- 4.1 Optimization Algorithms.- 4.2 Conjugate Gradient.- 4.3 Discrete Stability.- 4.4 Fluid Dynamics.- 4.5 Lax Wendroff Scheme.- 4.6 Pseudo Eigenvalues.- Endnotes for Chapter 4.- 5 Finite Dimensions.- 5.1 Value Field.- 5.2 Gersgorin Sets.- 5.3 Radius Estimates.- 5.4 Hadamard Product.- 5.5 Generalized Ranges.- 5.6 W(A) Computation.- Endnotes for Chapter 5.- 6 Operator Classes.- 6.1 Resolvent Growth.- 6.2 Three Classes.- 6.3 Spectral Sets.- 6.4 Normality Conditions.- 6.5 Finite Inclusions.- 6.6 Beyond Spectraloid.- Endnotes for Chapter 6.
Bibliographische Angaben
- Autoren: Karl E. Gustafson , Duggirala K. M. Rao
- 1996, Softcover reprint of the original 1st ed. 1997., 190 Seiten, 11 farbige Abbildungen, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 038794835X
- ISBN-13: 9780387948355
Sprache:
Englisch
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