# Best approximation in inner product spaces

##### By: Deutsch, Frank R.

Material type: BookSeries: 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/9780387951560Item type | Current location | Item location | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|---|

Books | Vikram Sarabhai Library General Stacks | Slot 1381 (0 Floor, East Wing) | Non-fiction | 515.733 D3B3 (Browse shelf) | Checked out | 26/03/2020 | 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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