Computational functional analysis

Cover......Page 1
COMPUTATIONAL FUNCTIONALANALYSIS, Second Edition......Page 3
ISBN-13: 978-1-904-275-24-4......Page 4
Table of Contents......Page 6
Preface......Page 10
Acknowledgements......Page 11
Notation......Page 12
1  Introduction......Page 14
2  Linear spaces......Page 16
3  Topological spaces......Page 20
4  Metric spaces......Page 24
5  Normed linear spaces and Banach spaces......Page 28
6  Inner product spaces and Hilbert spaces......Page 32
7  Linear functionals......Page 41
8  Types of convergence in function spaces......Page 45
9  Reproducing kernel Hilbert spaces......Page 48
10  Order relations in function spaces......Page 55
11  Operators in function spaces......Page 62
Neumann series......Page 66
Adjoint operators......Page 67
12  Completely continuous (compact) operators......Page 73
13  Approximation methods for linear operator equations......Page 81
1. Galerkin\'s method in Hilbert spaces......Page 89
2. Collocation methods......Page 90
3. Finite difference methods......Page 91
14  Interval methods for operator equations......Page 96
15  Contraction mappings and iterative methods for operator equations in fixed point form......Page 107
16  Frkhet derivatives......Page 115
17  Newtons method in Banach spaces......Page 129
18  Variants of Newtons method......Page 144
19  Homotopy and continuation methods......Page 151
Davidenkos method......Page 156
Computational aspects......Page 157
20  A hybrid method for a free boundary problem......Page 159
Hints for selected exercises......Page 173
Further reading......Page 186
INDEX......Page 190