Best Approximation in Inner Product Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2001
|
| Schriftenreihe: | CMS Books in Mathematics / Ouvrages de mathématiques de la SMC
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 338 p) |
| ISBN: | 9781468492989 9781441928900 |
| ISSN: | 1613-5237 |
| DOI: | 10.1007/978-1-4684-9298-9 |
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Datensatz im Suchindex
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| author | Deutsch, Frank |
| author_facet | Deutsch, Frank |
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| author_sort | Deutsch, Frank |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-9298-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468492989 9781441928900 |
| issn | 1613-5237 |
| language | English |
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| spelling | Deutsch, Frank Verfasser aut Best Approximation in Inner Product Spaces by Frank Deutsch New York, NY Springer New York 2001 1 Online-Ressource (XVI, 338 p) txt rdacontent c rdamedia cr rdacarrier CMS Books in Mathematics / Ouvrages de mathématiques de la SMC 1613-5237 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 Mathematics Computer science Global analysis (Mathematics) Analysis Mathematics of Computing Informatik Mathematik Innenproduktraum (DE-588)4130366-0 gnd rswk-swf Beste Approximation (DE-588)4144932-0 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s Innenproduktraum (DE-588)4130366-0 s 1\p DE-604 Beste Approximation (DE-588)4144932-0 s 2\p DE-604 https://doi.org/10.1007/978-1-4684-9298-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deutsch, Frank Best Approximation in Inner Product Spaces Mathematics Computer science Global analysis (Mathematics) Analysis Mathematics of Computing Informatik Mathematik Innenproduktraum (DE-588)4130366-0 gnd Beste Approximation (DE-588)4144932-0 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4130366-0 (DE-588)4144932-0 (DE-588)4120913-8 |
| title | Best Approximation in Inner Product Spaces |
| title_auth | Best Approximation in Inner Product Spaces |
| title_exact_search | Best Approximation in Inner Product Spaces |
| title_full | Best Approximation in Inner Product Spaces by Frank Deutsch |
| title_fullStr | Best Approximation in Inner Product Spaces by Frank Deutsch |
| title_full_unstemmed | Best Approximation in Inner Product Spaces by Frank Deutsch |
| title_short | Best Approximation in Inner Product Spaces |
| title_sort | best approximation in inner product spaces |
| topic | Mathematics Computer science Global analysis (Mathematics) Analysis Mathematics of Computing Informatik Mathematik Innenproduktraum (DE-588)4130366-0 gnd Beste Approximation (DE-588)4144932-0 gnd Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Mathematics Computer science Global analysis (Mathematics) Analysis Mathematics of Computing Informatik Mathematik Innenproduktraum Beste Approximation Approximationstheorie |
| url | https://doi.org/10.1007/978-1-4684-9298-9 |
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