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Tables of Contents for Numerical Analysis of Wavelet Methods
Chapter/Section Title
Page #
Page Count
Introduction
xi
Notations
xvii
Basic examples
1
42
Introduction
1
1
The Haar system
2
8
The Schauder hierarchical basis
10
6
Multivariate constructions
16
6
Adaptive approximation
22
11
Multilevel preconditioning
33
7
Conclusions
40
1
Historical notes
41
2
Multiresolution approximation
43
112
Introduction
43
2
Multiresolution analysis
45
12
Refinable functions
57
6
Subdivision schemes
63
7
Computing with refinable functions
70
4
Wavelets and multiscale algorithms
74
9
Smoothness analysis
83
6
Polynomial exactness
89
5
Duality, orthonormality and interpolation
94
5
Interpolatory and orthonormal wavelets
99
8
Wavelets and splines
107
13
Bounded domains and boundary conditions
120
11
Point values, cell averages, finite elements
131
19
Conclusions
150
1
Historical notes
151
4
Approximation and smoothness
155
88
Introduction
155
4
Function spaces
159
6
Direct estimates
165
6
Inverse estimates
171
3
Interpolation and approximation spaces
174
8
Characterization of smoothness classes
182
5
Lp-unstable approximation and 0 < p < 1
187
12
Negative smoothness and Lp-spaces
199
9
Bounded domains
208
8
Boundary conditions
216
10
Multilevel preconditioning
226
13
Conclusions
239
1
Historical notes
240
3
Adaptivity
243
78
Introduction
243
5
Nonlinear approximation in Besov spaces
248
6
Nonlinear wavelet approximation in Lp
254
8
Adaptive finite element approximation
262
5
Other types of nonlinear approximations
267
9
Adaptive approximation of operators
276
13
Nonlinear approximation and PDE's
289
7
Adaptive multiscale processing
296
10
Adaptive space refinement
306
11
Conclusions
317
1
Historical notes
318
3
References
321
14
Index
335