Computational Functional Analysis

ISBN-13: 9781904275244 / Angielski / Miękka / 2007 / 212 str.

Ramon E Moore (Ohio State University); USA) Michael J Cloud (Lawrence Technological University

Opis

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.

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

Recenzje

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

Spis treści

• 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