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Best approximation in inner product spaces

By: Deutsch, Frank R.
Material type: materialTypeLabelBookSeries: CMS Books in Mathematics. Publisher: New York Springer 2001Description: xv, 338p. With index.ISBN: 9780387951560.Subject(s): Approximation theory | Inner product spaces | Mathematics | Computer science | Global analysis (Mathematics)DDC classification: 515.733 Summary: 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. https://www.springer.com/in/book/9780387951560
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Slot 1381 (0 Floor, East Wing) Non-fiction 515.733 D3B3 (Browse shelf) Checked out 27/11/2019 199061

Table of contents (12 chapters)
Inner Product Spaces Pages 1-19

Best Approximation Pages 21-32

Existence and Uniqueness of Best Approximations Pages 33-41

Characterization of Best Approximations Pages 43-70

The Metric Projection Pages 71-87

Bounded Linear Functionals and Best Approximation from Hyperplanes and Half-Spaces Pages 89-123

Error of Approximation Pages 125-153

Generalized Solutions of Linear Equations Pages 155-192

The Method of Alternating Projections Pages 193-235

Constrained Interpolation from a Convex Set Pages 237-285

Interpolation and Approximation Pages 287-299

Convexity of Chebyshev Sets Pages 301-309

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.

https://www.springer.com/in/book/9780387951560

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