Page 9 - Compact Numerical Methods For Computers

PREFACE TO THE FIRST EDITION

This book is designed to help people solve numerical problems. In particular, it is
directed to those who wish to solve numerical problems on ‘small’ computers, that
is, machines which have limited storage in their main memory for program and
data. This may be a programmable calculator-even a pocket model-or it may
be a subsystem of a monster computer. The algorithms that are presented in the
following pages have been used on machines such as a Hewlett-Packard 9825
programmable calculator and an IBM 370/168 with Floating Point Systems Array
Processor. That is to say, they are designed to be used anywhere that a problem
exists for them to attempt to solve. In some instances, the algorithms will not be
as efficient as others available for the job because they have been chosen and
developed to be ‘small’. However, I believe users will find them surprisingly
economical to employ because their size and/or simplicity reduces errors and
human costs compared with equivalent ‘larger’ programs.
Can this book be used as a text to teach numerical methods? I believe it can.
The subject areas covered are, principally, numerical linear algebra, function
minimisation and root-finding. Interpolation, quadrature and differential equa-
tions are largely ignored as they have not formed a significant part of my own
work experience. The instructor in numerical methods will find perhaps too few
examples and no exercises. However, I feel the examples which are presented
provide fertile ground for the development of many exercises. As much as
possible, I have tried to present examples from the real world. Thus the origins of
the mathematical problems are visible in order that readers may appreciate that
these are not merely interesting diversions for those with time and computers
available.
Errors in a book of this sort, especially in the algorithms, can depreciate its
value severely. I would very much appreciate hearing from anyone who discovers
faults and will do my best to respond to such queries by maintaining an errata
sheet. In addition to the inevitable typographical errors, my own included, I
anticipate that some practitioners will take exception to some of the choices I
have made with respect to algorithms, convergence criteria and organisation of
calculations. Out of such differences, I have usually managed to learn something
of value in improving my subsequent work, either by accepting new ideas or by
being reassured that what I was doing had been through some criticism and had
survived.
There are a number of people who deserve thanks for their contribution to this
book and who may not be mentioned explicitly in the text:
(i) in the United Kingdom, the many members of the Numerical Algorithms
Group, of the Numerical Optimization Centre and of various university depart-
ments with whom I discussed the ideas from which the algorithms have con-
densed;
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