Best Approximation in Inner Product Spaces
By: by Frank Deutsch
Series: CMS Books in Mathematics / Ouvrages de mathématiques de la SMC, 1613-5237; CMS Books in Mathematics / Ouvrages de mathématiques de la SMC
Publisher: Springer New York
Published: 2001
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 338
ISBN-13: 9781468492989
Description: This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective. The book is based on lecture notes for a graduate course on best approximation which the author has taught for over 25 years.
Table of contents: title: Inner Product Spaces; title: Best Approximation; title: Existence and Uniqueness of Best Approximations; title: Characterization of Best Approximations; title: The Metric Projection; title: Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-spaces; title: Error of Approximation; title: Generalized Solutions of Linear Equations; title: The Method of Alternating Projections; title: Constrained Interpolation from a Convex Set; title: Interpolation and Approximation; title: Convexity of Chebyshev Sets.