Book123

    Free register and download UseNet downloader, then you can FREE Download from UseNet.

    Download without Limit " Technical The Approximate Minimization of Functionals " from UseNet for FREE!

More

James W. Daniel, "The Approximate Minimization of Functionals"

PREFACE

This material was prepared for use as a text in support of my lectures at the

1969 session on "Minimization problems" of l'Ecole d'Ete Analyse Numerique

held at Le Breau-sans-Nappe, France, and sponsored by the Commissariat

a l'Energie Atomique, Gaz de France, and l'Electricite de France; I gratefully

acknowledge the financial support of those organizations and their cooperation

in reproducing this text. Of course those ideas in this text which are

primarily the author's did not come to light only during the period of writing;

therefore I must also acknowledge several other sources of support in recent

years, particularly the National Science Foundation, the- Office of Naval

Research, the Mathematics Research left at the University of Wisconsin,

and the Computer Sciences Department at the University of Wisconsin,

Madison. It is a great pleasure fpr me to acknowledge the invaluable cooperation

of my three assistants at I'Ecole d'Ete, Mssrs. Chavent, Yvon, and

Tremolieres, and the students there, especially Mr. Lascaux, whose questions,

comments, and suggestions were of great help to me.

This book represents an attempt at a general presentation of problems

involved in the approximate minimization of functionals. As such it treats

in the first chapter the general area of variational problems and the question

of the existence of solutions, in the next two chapters the question of the

convergence of approximate solutions of discretized variational problems in

general and in specific important cases, in the next two chapters the theory

of gradient methods of minimization in general spaces, and in the final four

chapters practical computational methods of minimization in ER'. Although

a significant amount of material is presented concerning constrained minimization

problems, the primary emphasis of this text is on unconstrained

problems, particularly in the last four chapters; this is not a text on mathematical programming. In the last four chapters on "practical" methods,

detailed computational algorithms or computer programs are not presented.

The rather "theoretical" presentation of this "practical" material reflects my

feeling that analysis and understanding of an algorithm, even under specialized

hypotheses, is all-important in the creation of new methods; whenever possible,

however, the references include sources of computer programs or

detailed computational descriptions of the implementations of algorithms.

The references presented here give a reasonably thorough coverage of

the most important English language literature on minimization methods,

although no claim is made of completeness. Although many of the important

results of Russian papers can also be found in English, the largest gaps in the

references are with respect to the very extensive literature in Russian. I hope

to correct this shortcoming at some future time.

JAMES W. DANIEL

Madison, Wisconsin

Buy Book at Lowest Price on Amazon

Download

Rating:
2.5 out of 5 by Book123