search for books and compare prices
Tables of Contents for Spectral Computations for Bounded Operators
Chapter/Section Title
Page #
Page Count
Preface
ix
 
Notation
xiii
 
Spectral Decomposition
1
68
General Notions
1
20
Decompositions
21
12
Spectral Sets of Finite Type
33
8
Adjoint and Product Spaces
41
23
Adjoint Space
41
7
Product Space
48
16
Exercises
64
5
Spectral Approximation
69
44
Convergence of Operators
69
7
Property U
76
5
Property L
81
9
Error Estimates
90
16
Exercises
106
7
Improvement of Accuracy
113
72
Iterative Refinement
114
34
General Remarks
114
5
Refinement Schemes for a Simple Eigenvalue
119
15
Refinement Schemes for a Cluster of Eigenvalues
134
14
Acceleration
148
33
Motivation
148
8
Higher Order Spectral Approximation
156
6
Simple Eigenvalue and Cluster of Eigenvalues
162
14
Dependence on the Order of the Spectral Analysis
176
5
Exercises
181
4
Finite Rank Approximations
185
62
Approximations Based on Projections
185
14
Truncation of a Schauder Expansion
187
3
Interpolatory Projections
190
5
Orthogonal Projections on Subspaces of Piecewise Constant Functions
195
2
Finite Element Approximation
197
2
Approximations of Integral Operators
199
31
Degenerate Kernel Approximation
200
3
Approximations Based on Numerical Integration
203
19
Weakly Singular Integral Operators
222
8
A Posteriori Error Estimates
230
10
Exercises
240
7
Matrix Formulations
247
68
Finite Rank Operators
248
27
Singularity Subtraction
257
7
Uniformly Well-Conditioned Bases
264
11
Iterative Refinement
275
7
Acceleration
282
18
Numerical Examples
300
9
Exercises
309
6
Matrix Computations
315
58
QR factorization
316
11
Householder symmetries
319
5
Hessenberg Matrices
324
3
Convergence of a Sequence of Subspaces
327
9
Basic Definitions
327
4
Krylov Sequences
331
5
QR Methods and Inverse Iteration
336
8
The Francis-Kublanovskaya QR Method
336
6
Simultaneous Inverse Iteration Method
342
2
Error Analysis
344
29
Condition Numbers or Forward Error Analysis
344
3
Stability or Backward Error Analysis
347
15
Relative Error in Spectral Computations and Stopping Criteria for the Basic QR Method
362
7
Relative Error in Solving a Sylvester Equation
369
4
References
373
6
Index
379