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Best Approximation in Inner Product Spaces

Best Approximation in Inner Product Spaces


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About the Book

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.


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Product Details
  • ISBN-13: 9780387951560
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Depth: 19
  • Language: English
  • Returnable: N
  • Spine Width: 21 mm
  • Width: 156 mm
  • ISBN-10: 0387951563
  • Publisher Date: 20 Apr 2001
  • Binding: Hardback
  • Height: 234 mm
  • No of Pages: 338
  • Series Title: CMS Books in Mathematics
  • Weight: 730 gr


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