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Full Description
This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ''hybrid'' method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ''We learn by doing'' is reflected throughout the book.
Contents
Preface
Acknowledgements
Notation
1: Introduction
2: Linear spaces
3: Topological spaces
4: Metric spaces
5: Normed linear spaces and Banach spaces
6: Inner product spaces and Hilbert spaces
7: Linear functionals
8: Types of convergence in function spaces
9: Reproducing kernel Hilbert spaces
10: Order relations in function spaces
11: Operators in function spaces
Neumann series
Adjoint operators
12: Completely continuous (compact) operators
13: Approximation methods for linear operator equations
14: Interval methods for operator equations
15: Contraction mappings and iterative methods for operator equations in fixed point form
16: Fréchet derivatives
17: Newton's method in Banach spaces
18: Variants of Newton's method
Numerical examples
19: Homotopy and continuation methods
Davidenko's method
Computational aspects
20: A hybrid method for a free boundary problem
Hints for selected exercises
Further reading
Index
