A Course on Optimization and Best Approximation
- PDF / 223,329 Bytes
- 7 Pages / 504 x 720 pts Page_size
- 23 Downloads / 258 Views
257 Richard B. Holmes Purdue University, Lafayette, IN/USA
A Course on
Optimization and Best Approximation
Springer-Verlag Berlin-Heidelberg • NewYork 1 972
A M S S u b j e c t Classifications (1970): 41-02, 41 A 50, 41 A 65, 4 6 B 9 9 , 4 6 N 0 5 , 49-02, 4 9 B 30, 9 0 C 2 5
I S B N 3-540-05764-1 S p r i n g e r - V e r l a g B e r l i n • H e i d e l b e r g • N e w Y o r k I S B N 0-387-05764-1 S p r i n g e r - V e r l a g N e w Y o r k • H e i d e l b e r g • B e r l i n
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. @ by Springer-Verlag Berlin * Heidelberg 1972. Library of Congress Catalog Card Number 70-189753. Printed in Germany. Offsetdmck: Julius Beltz, Hemsbach/Bergstr.
PREFACE
The course for which these notes were originally prepared was a one-semester graduate level course at Purdue University, dealing with optimization in general and best approximation in particular. The prerequisites were modest:
a semester's worth of functional
analysis together with the usual background required for such a course.
A few prerequisite results of special importance have been
gathered together for ease of reference in Part I. My general aim was to present an interesting field of application of functional analysis.
Although the tenor of the course is
consequently rather theoretical,
I made some effort to include a
few fairly concrete examples, and to bring under consideration problems of genuine practical interest. are convex programs
(~'s 11-13), calculus of variations
minimum effort control
(§21), quadrature formulas
of "good" approximations to functions estimation from inadequate data linear systems
Examples of such problems
(§'s 34-3S).
(§17),
(§24), construction
(§'s 26 and 29), optimal
(§33), solution of various ill-posed
Indeed, the bulk of the notes is devoted
to a presentation of the theoretical background needed for the study of such problems. No attempt has been made to provide encyclopedic coverage of the various topics.
Rather I tried only to show some highlights,
techniques~ and examples in each of the several areas studied. Should a reader be stimulated to pursue a particular topic further, he will hopefully find an adequate sample of the pertinent literature included in the bibliographies.
(Note that in addition to the main
bibliography between Parts IV and V, each section in Part V has its own special set of references appended.)
IV The first fleshed-out course. about
three parts
arrangement
That course
of the material
also involved
50 of those problems
contains
hints
portion
pages
and/or
of the notes
indicated
I feel been
inclu
Data Loading...
