Real Computing Made Real

275 Pages·1995·20.98 MB·English

by  Forman S. Acton

REAL
Computing
Made
REAL
Preventing Errors in Scientific and
Engineersg Calculations
Princeton University Press
Princeton, New Jersey
Copyright @ 1996 by Princeton University Press
Published by Prince ton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
Chichester, West Sussex
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Acton, Forman S.
REAL Computing made real : preventing errors in scientific and
engineering calculations / Forman S. Acton.
cm.
P.
Includes Index.
ISBN 0-691-03663-2 (alk. paper)
1. Error analysis (Mathematics) 2. Numerical analysis-Data
processing. I. Title.
QA275.A25 1996
519.4'0285'5 1 d c 2 0 95- 10 606
CIP
This book has been composed in Stempel Schneidler, Flintstone and Lucida Sans
The publisher would like to acknowledge Forman Acton for providing the
camera-ready copy from which this book was printed
Text Design by C. Alvarez
Princeton University Press books are printed on acid-free paper and meet the
guidelines for permanence and durability of the Committee on Production
Guidelines for Book Longevity of the Council on Library Resources
Frontispiece. Courtesy of the Freer Gallery of Art, Washington, D.C. 98.423:
An Actor in Character by Katsukawa Shunko (1743-1812) Japan, Edo period.
Detail from a painting; color, lacquer black on silk: 58.7 x 26.8 cm.
All other photographs courtesy of Phisit Phisitthakorn
Printed in the United States of America
by Princeton Academic Press
CONTENTS
AN EXHORTATION
Make fewer errors! (Errors are hard to find.) We
need help - but much software obscures! - A
kind of Kyrie.
VI Contents
Chapter 0
TOOLS OF W E TRADE
A brief collection of those useful numerical aids
that may by now have faded slightly in your
memory.
A WORKSHOP FOR PRACTICE IN
SKETCHING FUNCTIONS
....
to refresh your skills at getting realistic pic-
tures of your equations (and their parts). Sketch-
ing an equation before an algorithm is chosen
will prevent more computational disasters than
any other effort. Try some! (We give our own
at the end of this chapter.)
GLOOMY MUSINGS 63
.. . .
Correctness, Efficiency and Responsibility
How can we get into the habit of thinking care-
fully about our computations before writing our
programs+ How can we be sensitized to pe-
venting errors without becoming paralyzed into
inaction+ Can we ever learn to distrust s o b a r e
even while using itt - a Dies Irae!
Chapter 1
W I N E A R EQUATIONS
We seek rearrangements of the equation to per-
mit iterations that approach roots from one side.
A picture will usually lead to an algorithm that
does not degenerate into futile repetitions. (It
may also show that you are about to seek a so-
lution that you really don't want!)
Contents MI
Chapter 2
PRESERVING SIGMFICAW DIGITS
-
When significant digits disappear, pay heed
for your algorithm is often about to break down!
Searching for these places will lead you to trou-
ble spots and allow you to fix them before they
rise to bite you. This error-prevention dividend
is far more important than the digits that could
be lost. We illustrate various techniques, and
include a real-life problem.
Chapter 3
QUADRATURES
A field where it often pays to alter the problem
to fit the algorithm: How to remove singularities
that can spawn monumental algorithmic ineffi-
ciencies.
Chapter 4
RECURRENCE RELAIONS
A hands-on introduction to a delightfully simple
and efficient class of algorithms - that don't
always work! A world where molehills really
do sometimes become mountains.
Chapter 5
CHOOSING AM) 'TUMNG AN ALGORITHM
We follow a straightforward small problem thru
our search for suitable algorithms - and are per-
haps surprised to find the process rather convo-
luted.
ANSWERS TO MOST OF THE EXERCISES 205
- Dona Nobis Pacem!

ACKNOWLEDGMENTS
Altho A.P.C. long served to cure headaches, the present team of Ac-
ton, Phisit, and Carmina have here delivered a book that may produce
them! Let me therefore quickly declare that the designer, Carmina
Alvarez, is responsible for wonderfully turning the author's penchant
for oriental statues into a coherent visual style that uses some of the
seventy-three photographs taken, on very short notice, by my friend
Phisit Phisitthakorn, architect, of Bangkok. But neither of them can
be blamed for the verbal content, which was created entirely by your
author.*
I would also like to thank Jane Low who led the production team
at the Princeton University Press and Trevor Lipscombe, the Physical
Sciences Editor, who gallantly sponsored the book even after I con-
cluded that a few Shavian simplified spellings were too ingrained by
my fifty-five years of use to be expunged now.
*
Of course the text is error-free - but you report any you find to acton@princeton edu