Best Approximation in Inner Product Spaces

Frank R. Deutsch

ISBN 10: 1441928901 / ISBN 13: 9781441928900

Edité par Springer New York, Springer US, 2010

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9781441928900

Détails bibliographiques

• Titre: Best Approximation in Inner Product Spaces
• Éditeur: Springer New York, Springer US
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 1441928901
• ISBN à 13 chiffres: 9781441928900
• Reliure: Taschenbuch
• État de l'article: Neu

A propos de ce titre

Synopsis

This is the first systematic study of best approximation theory in inner product spaces and, in particular, in Hilbert space. Geometric considerations play a prominent role in developing and understanding the theory. The only prerequisites for reading the book is some knowledge of advanced calculus and linear algebra. Throughout the book, examples and applications have been interspersed with the theory. Each chapter concludes with numerous exercises and a section in which the author puts the results of that chapter into a historical perspective.