Computational Functional Analysis

Häftad, Engelska, 2007

Av Ramon E Moore, Michael J Cloud, Ramon E. Moore, Michael J. Cloud

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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.

Produktinformation

Utgivningsdatum2007-06-01
Mått160 x 234 x 10 mm
Vikt310 g
FormatHäftad
SpråkEngelska
Antal sidor212
Upplaga2
FörlagElsevier Science & Technology
ISBN9781904275244

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Preface AcknowledgementsNotation1: Introduction2: Linear spaces3: Topological spaces4: Metric spaces5: Normed linear spaces and Banach spaces6: Inner product spaces and Hilbert spaces7: Linear functionals8: Types of convergence in function spaces9: Reproducing kernel Hilbert spaces10: Order relations in function spaces11: Operators in function spaces Neumann seriesAdjoint operators12: Completely continuous (compact) operators13: Approximation methods for linear operator equations14: Interval methods for operator equations15: Contraction mappings and iterative methods for operator equations in fixed point form16: Fréchet derivatives17: Newton’s method in Banach spaces18: Variants of Newton’s method Numerical examples19: Homotopy and continuation methods Davidenko’s methodComputational aspects20: A hybrid method for a free boundary problemHints for selected exercisesFurther readingIndex