Ahues / Largillier / Limaye Spectral Computations for Bounded Operators

Erscheinungsjahr 2010
ISBN: 978-1-4200-3582-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 400 Seiten

Reihe: Applied Mathematics

Exact eigenvalues, eigenvectors, and principal vectors of operators with infinite dimensional ranges can rarely be found. Therefore, one must approximate such operators by finite rank operators, then solve the original eigenvalue problem approximately. Serving as both an outstanding text for graduate students and as a source of current results for research scientists, Spectral Computations for Bounded Operators addresses the issue of solving eigenvalue problems for operators on infinite dimensional spaces.

From a review of classical spectral theory through concrete approximation techniques to finite dimensional situations that can be implemented on a computer, this volume illustrates the marriage of pure and applied mathematics. It contains a variety of recent developments, including a new type of approximation that encompasses a variety of approximation methods but is simple to verify in practice. It also suggests a new stopping criterion for the QR Method and outlines advances in both the iterative refinement and acceleration techniques for improving the accuracy of approximations. The authors illustrate all definitions and results with elementary examples and include numerous exercises.

Spectral Computations for Bounded Operators thus serves as both an outstanding text for second-year graduate students and as a source of current results for research scientists.

Zielgruppe

Graduate students and researchers in applied mathematics working in the fields of functional and numerical analysis; scientists and engineers in fields including heat transfer, quantum mechanics, and high-speed computing

Autoren/Hrsg.

Ahues, Mario

Largillier, Alain

Limaye, Balmohan

Fachgebiete

• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

SPECTRAL DECOMPOSITION
Genera Notions
Decompositions
Spectral Sets of Finite Type
Adjoint and Product Spaces
SPECTRAL APPROXIMATION
Convergence of operators
Property U
Property L
Error Estimates
IMPROVEMENT OF ACCURACY
Iterative Refinement
Acceleration
FINITE RANK APPROXIMATIONS
Approximations Based on Projection
Approximations of Integral Operators
A Posteriori Error Estimates
MATRIX FORMULATIONS
Finite Rank Operators
Iterative Refinement
Acceleration
Numerical Examples
MATRIX COMPUTATIONS
QR Factorization
Convergence of a Sequence of Subspaces
QR Methods and Inverse Iteration
Error Analysis
REFERENCES
INDEX

Each chapter also includes exercises