Best Approximation in Inner Product Spaces Softcover Repri Edition Contributor(s): Deutsch, Frank R. (Author) |
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ISBN: 1441928901 ISBN-13: 9781441928900 Publisher: Springer
Binding Type: Paperback - See All Available Formats & Editions Published: December 2010 Click for more in this series: CMS Books in Mathematics |
Additional Information |
BISAC Categories: - Mathematics | Transformations - Mathematics | Mathematical Analysis - Computers | Computer Science |
Dewey: 515.733 |
Series: CMS Books in Mathematics |
Physical Information: 0.74" H x 6.14" W x 9.21" L (1.10 lbs) 338 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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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