Spectral Computations for Bounded Operators

Spectral Computations for Bounded Operators

By (author)  , By (author)  , By (author) 

Free delivery worldwide

Available. Dispatched from the UK in 2 business days
When will my order arrive?

Description

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.
show more

Product details

  • Hardback | 400 pages
  • 161 x 245.9 x 27.4mm | 730.3g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 1448 equations; 18 Tables, black and white; 150 Illustrations, black and white
  • 1584881968
  • 9781584881964

Table of contents

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
show more

Review quote

"This book gives a careful account of the theory underlying methods for numerical computation of approximations of eigenvalues, eigenvectors and generalized eigenvectors of bounded linear operators in infinite-dimensional space. The authors have been substantial contributors to the field, and the book gives some emphasis to topics on which they have worked. . . As well as being a valuable reference for mathematicians working on the development of analysis of numerical methods, the book is also suitable as a graduate text for students who have done a first course on functional analysis." -Alan L. Andrews
show more