## Introduction to Numerical Methods and Optimization Techniques Book

Elsevier Science Ltd | 1978 | ISBN: 0444002634 | 308 pages | PDF | 3,7 MB

The availability of computers has revolutionized every field which depends

on numerical calculations. The scientist or engineer can be greatly aided in

his work if he knows how to enlist the aid of his new ally. The purpose of

this book is to help the undergraduate student learn how to apply a

computer to many different types of practical problems. The book is

written in a manner that should instill enthusiasm in the reader and help

convince him that the computer is one of the greatest labor saving devices

ever to come along.

This book's philosophy differs from most others written on numerical

methods or numerical analysis. In a typical numerical-analysis text, much

time is spent on error analysis. However, in practical applications, usually

little time is devoted to rigorous error analysis.

Instead of relying solely on error analysis to estimate the accuracy of

answers, other methods are emphasized in this text. Observing how a

process converges can give insight into its accuracy. Also, solving a

problem two different ways can verify a solution. Although error analysis

is not very practical as a tool for estimating accuracy, it does have other

uses. It can be used to compare different numerical methods and demonstrate

that, on the average, one is superior to another. Or a knowledge of

error properties can be used to improve a numerical method.

Avoiding a lengthy investigation of error analysis allows time for the

reader to become acquainted with optimization techniques. Numerical

methods and optimization techniques are intimately related, but unfortunately

they are not generally taught in the same course. However, since

both numerical methods and optimization techniques are usually iterative

procedures, they have a common philosophy and application. In fact, as

demonstrated in this book, an optimization technique can be viewed as a

collection of numerical methods which have been linked together in a

specific way. Thus, once a student has become familiar with numerical

methods the extension to optimization techniques is very natural.

This text does not attempt to be a complete catalog of numerical

methods or optimization techniques-volumes would be needed for this.

For a specific problem, the specialist can probably consult the literature

and obtain a more efficient solution than presented in this book. If he uses

his sophisticated program very often, his time is well spent. In fact, this

text is not written for the specialist, but for the reader or student who will

probably not have the luxury of spending days on research to save

milliseconds of computer time.

Instead of overwhelming the reader with numerous methods for solving

the same problem, attention is focused on one or two. If a person is

familiar and confident with a specific method, he is much more likely to

apply it than if he only has a nodding acquaintance. Just because a

particular method has been included in this text, it need not be the best

one available. The choices were influenced by the desire to have an

introductory text which links numerical methods to optimization techniques.

At the end of most chapters is a section entitled "Suggested

Reading in Related Topics", which enables the enthusiastic reader to do

additional research on topics not essential to an introductory course.

The typical student using this book for a formal course will be a junior

or senior-a sophomore could understand the material, but might not

appreciate the range of applications. A knowledge of differentiation and

integration is essential for the course; the ability to solve differential

equations would be helpful, but is not essential.

Because the application of many of the algorithms in this text requires

the use of a computer, numerous programs are included. These programs

are written in a version of time-sharing FORTRAN that is similar to FORTRAN

iv. The programs were all run on a Control Data Cyber 70 computer

system.

The programs that have been included in the text are written with the

emphasis on clarity. Their purpose is to implement the methods described

in the text and provide a means for the student to apply the algorithms.

The programs have not been included in the hope that they will become

widely used in various computation centers; they are ill suited for that

purpose. The literature contains ample selections of programs that have

been written with the emphasis on speed and accuracy. However, even

though the programs in this book are relatively simple, they should be

adequate for the problems encountered by students who are at this

introductory level; and they provide a good basis for understanding the

more sophisticated programs that abound in the literature.

The problems at the end of the chapters serve various purposes. Some

help to extend the material presented in the text or to check the reader's

knowledge of subtle points. Others illustrate the application of the programs

or equations. Finally, many of the problems help the student

become familiar with the computer so that it will become an ally in future

endeavors.

The idea of combining numerical methods and optimization techniques

into one text occurred to the author while teaching at Tennessee State

University. My appreciation goes to those students who helped shape the

early direction of the book. Also, I have the good fortune to have had

many different experts review the text and offer numerous suggestions for

its improvement. To two of my colleagues go special thanks: R. P. Snicer

for his thorough review and detailed suggestions, and P. H. McDonald for

her helpful hints on structured programming.

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