Computational functional analysis

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-l.

Cover; COMPUTATIONAL FUNCTIONAL ANALYSIS; Copyright; Table of Contents; Preface; Notation; 1 Introduction; 2 Linear spaces; Exercise 1; Exercise 2; Exercise 3; Exercise 4; Exercise 5; Exercise 6; Exercise 7; Exercise 8; Exercise 9; 3Topological spaces; Exercise 10; Exercise 11; Exercise 12; 4Metric spaces; Exercise 13; Exercise 14; Exercise 15; Exercise 16; Exercise 17; Exercise 18; Exercise 19; Exercise 20; Exercise 21; 5 Normed linear spaces and Banach spaces; Exercise 22; Exercise 23; Exercise 24; Exercise 25; Exercise 26; Exercise 27; Exercise 28; 6 Inner product spaces and Hilbert spaces.

Exercise 29Exercise 30; Exercise 31; Exercise 32; Exercise 33; Exercise 34; Exercise 35; Exercise 36; Exercise 37; Exercise 38; Exercise 39; 7 Linear functionals; Exercise 40; Exercise 41; Exercise 42; Exercise 43; Exercise 44; Exercise 45; 8 Types of convergence in function spaces; Exercise 46; Exercise 47; Exercise 48; Exercise 49; Exercise 50; Exercise 51; Exercise 52; 9 Reproducing kernel Hilbert spaces; Exercise 53; Exercise 54; Exercise 55; Exercise 56; Exercise 57; 10 Order relations in function spaces; Exercise 58; Exercise 59; Exercise 60; Exercise 61; Exercise 62; Exercise 63.

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