Computational Functional Analysis - 2nd Edition - ISBN: 9781904275244, 9780857099433

Computational Functional Analysis

2nd Edition

Authors: Ramon Moore Michael Cloud
Paperback ISBN: 9781904275244
eBook ISBN: 9780857099433
Imprint: Woodhead Publishing
Published Date: 1st June 2007
Page Count: 212
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Description

  • 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

Key Features

  • Contains 100 problem-exercises, answers and tutorial hints for students reading applied functional analysis
  • Introduces interval analysis into the mainstream of computational functional analysis

Readership

First-year graduate-level students studying applied functional analysis or advanced engineering analysis and modern control theory

Table of 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

Details

No. of pages:
212
Language:
English
Copyright:
© Woodhead Publishing 2007
Published:
Imprint:
Woodhead Publishing
eBook ISBN:
9780857099433
Paperback ISBN:
9781904275244

About the Author

Ramon Moore

Ramon E. Moore, Ohio State University, USA.

Affiliations and Expertise

Ohio State University

Michael Cloud

Michael J. Cloud, Lawrence Technological University, USA.

Affiliations and Expertise

Lawrence Technological University, USA

Reviews

A stimulating and challenging introduction, (Review of the first edition) SIAM Review, USA, (William W. Hager, Pennsylvania State University).
A very readable introduction, excellent., The Mathematical Gazette