Computational functional analysis

✍ Scribed by Ramon E Moore

• Publisher: Horwood Pub
• Year: 2007
• Tongue: English
• Leaves: 202
• Series: Ellis Horwood series in mathematics and its applications
• Edition: 2ed.
• Category: Library

✦ Table of Contents

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