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Best Approximation in Inner Product Spaces

  • Frank Deutsch

Table of contents

  1. Front Matter
    Pages i-xv
  2. Frank Deutsch
    Pages 1-19
  3. Frank Deutsch
    Pages 21-32
  4. Frank Deutsch
    Pages 43-70
  5. Frank Deutsch
    Pages 71-87
  6. Frank Deutsch
    Pages 125-153
  7. Frank Deutsch
    Pages 155-192
  8. Frank Deutsch
    Pages 193-235
  9. Frank Deutsch
    Pages 237-285
  10. Frank Deutsch
    Pages 287-299
  11. Frank Deutsch
    Pages 301-309
  12. Back Matter
    Pages 311-338

About this book

Introduction

This book evolved from notes originally developed for a graduate course, "Best Approximation in Normed Linear Spaces," that I began giving at Penn State Uni­ versity more than 25 years ago. It soon became evident. that many of the students who wanted to take the course (including engineers, computer scientists, and statis­ ticians, as well as mathematicians) did not have the necessary prerequisites such as a working knowledge of Lp-spaces and some basic functional analysis. (Today such material is typically contained in the first-year graduate course in analysis. ) To accommodate these students, I usually ended up spending nearly half the course on these prerequisites, and the last half was devoted to the "best approximation" part. I did this a few times and determined that it was not satisfactory: Too much time was being spent on the presumed prerequisites. To be able to devote most of the course to "best approximation," I decided to concentrate on the simplest of the normed linear spaces-the inner product spaces-since the theory in inner product spaces can be taught from first principles in much less time, and also since one can give a convincing argument that inner product spaces are the most important of all the normed linear spaces anyway. The success of this approach turned out to be even better than I had originally anticipated: One can develop a fairly complete theory of best approximation in inner product spaces from first principles, and such was my purpose in writing this book.

Keywords

Convexity Hilbert space algorithms calculus compactness extrema linear algebra

Authors and affiliations

  • Frank Deutsch
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9298-9
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2890-0
  • Online ISBN 978-1-4684-9298-9
  • Series Print ISSN 1613-5237
  • Buy this book on publisher's site
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