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Best Approximation in Inner Product Spaces
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Best Approximation in Inner Product Spaces

Best Approximation in Inner Product Spaces

Jonathan M. Borwein, Peter B. Borwein, Frank Deutsch

338 pages, parution le 01/05/2001

Résumé

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 are 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.

Contents

  • Inner Product Spaces
  • Best Approximation
  • Existence and Uniqueness of Best Approximations
  • Characterization of Best Approximations
  • The Metric Projection
  • Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-spaces
  • Error of Approximation
  • Generalized Solutions of Linear Equations
  • The Method of Alternating Projections
  • Constrained Interpolation from a Convex Set
  • Interpolation and Approximation
  • Convexity of Chebyshev Sets

L'auteur - Peter B. Borwein

Peter Borwein is Professor of Mathematics at Simon Fraser University and the Associate Director of the Centre for Experimental and Constructive Mathematics. He is also the recipient of the Mathematical Association of America Chauvenet Prize and the Merten M. Hasse Prize for expository writing in mathematics.

L'auteur - Frank Deutsch

Frank Deutsch is professor of mathematics at the Pennsylvania State University. He is the author of over 85 research articles, and is an editor of five journals, including the Journal of Approximation Theory. He also was inducted into the Alumni Athletic Hall of Fame of the University of Hartford in 1996.

Caractéristiques techniques

  PAPIER
Éditeur(s) Springer
Auteur(s) Jonathan M. Borwein, Peter B. Borwein, Frank Deutsch
Parution 01/05/2001
Nb. de pages 338
Format 16 x 24
Couverture Relié
Poids 657g
Intérieur Noir et Blanc
EAN13 9780387951560

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