Java Number Cruncher: The Java Programmer's Guide to Numerical Computing - Softcover

Mak, Ronald

Softcover

ISBN 10: 0130460419 ISBN 13: 9780130460417

Publisher: Prentice Hall, 2002

Synopsis

Java Number Cruncher: The Java Programmer's Guide to Numerical Computing, by topic expert Ronald Mak, provides practical information for Java programmers who write mathematical programs. Without excessive mathematical theory, he animates the algorithms on the computer screen with interactive graphical programs and applets.

About this title

About the Author

RONALD MAK is a senior scientist at the Research Institute for Advanced Computer Science, located at the NASA Ames Research Center in California. He is currently designing Java-based enterprise software for the next Mars rover mission. He has degrees in the mathematical sciences and in computer science from Stanford University. His two previous books were on compiler writing.

From the Back Cover

• Non-theoretical explanations of practical numerical algorithms
• Algorithms in action with animated, interactive graphical Java programs and applets
• Computational errors and how to remove them from your code

Understand "computer math" and get the numbers you expect, reliably.

In Java Number Cruncher, author Ronald Mak explains how to spot-and how to avoid-the subtle programming miscues that can cause vexing calculation errors in your applications. An authority on mapping pure math to computer math, he explains how to use the often-overlooked computational features of Java, and does so in a clear, non-theoretical style.

Without getting lost in mathematical detail, you'll learn practical numerical algorithms for safely summing numbers, finding roots of equations, interpolation and approximation, numerical integration, solving differential equations, matrix operations, and solving sets of simultaneous equations. You'll also enjoy intriguing topics such as searching for patterns in prime numbers, generating random numbers, computing thousands of digits of pi, and creating intricately beautiful fractal images.

Java Number Cruncher includes:

• Practical information all Java programmers should know
• Popular computational algorithms in Java-without excessive mathematical theory
• Interactive graphical programs that bring the algorithms to life on the computer screen
• Rounding errors, the pitfalls of integer arithmetic, Java's implementation of the IEEE 754 floating-point standard, and more

This book is useful to all Java programmers, especially for those who want to learn about numerical computation, and for developers of scientific, financial, and data analysis applications.

Excerpt. © Reprinted by permission. All rights reserved.

Preface

The last time I looked, the Java programming language still had 1, 2, *, /, and % operators to do operations with numbers. It may be hard to believe today, but programming is not only about Web pages, graphics, enterprise software, database systems, and computer games.

I wrote this book to remind today's programmers, especially Java programmers, that computers really are quite good at numerical computing, affectionately known as "number crunching." In fact, some numerical computing underlies most programs—for example, not too many graphics applications or interactive computer games would get very far without crunching at least a few numbers. Of course, scientific, mathematical, statistical, and financial programs rely heavily on numerical computing.

So it behooves the typical Java programmer, besides knowing the standard API alphabet soup—JFC, RMI, JSP, EJB, JDBC, and so on—to know something about how to do good numerical computing. You'll never know when a roundoff error will bite you, or why that "correct" formula you copied right out of your favorite physics textbook into your program somehow computes the wrong answer.

Another reason I wrote this book is that I'm fascinated by the dichotomies of pure mathematics and computer science. On one hand, you have mathematics, a rigorous, abstract world where it is possible to prove, absolutely, that a computation is correct. On the other hand, you have computers, where computations are, well, they're fast. And yet, mathematicians and computer scientists can work together to devise some very clever ways to enable computers to do mathematics and, in the great majority of cases, to compute the right answer.

This book is an introduction to numerical computing. It is not a textbook on numerical methods or numerical analysis, although it certainly shows how to program many key numerical algorithms in Java. We'll examine these algorithms, enough to get a feel for how they work and why they're useful, without formally proving why they work. Because Java is ideal for doing so, we'll also demonstrate many of the algorithms with interactive, graphical programs. After seeing how we can dodge some of the pitfalls of floating-point and integer computations, we'll explore programs that solve equations for x, do interpolation and integration, solve differential equations and systems of linear equations, and more.

Numerical computing is not all work, either. This book also contains several chapters on lighter (but not necessarily less useful) topics, including computing thousands of digits of π, using different ways to generate random numbers, looking for patterns in the prime numbers, and creating the intricately beautiful fractal images.

I tried hard to keep the math in this book at the freshman calculus level or below—knowledge of high school algebra should be enough for most of it.

All the interactive programs in this book can run either as applets or as stand-alone programs. My friends and I have tested them with the Netscape 4.7 browser running on Windows, Linux, and Solaris, with Microsoft Internet Explorer 6.0 running on the PC, and Microsoft Internet Explorer 5.1 running on the Macintosh. I've tested the stand-alone programs on my Windows 98 PC with JDK 1.2, 1.3, and 1.4. Of course, there's no guarantee they'll all work perfectly for you, but the source code for all the programs, along with instructions on how to compile and run them, are available for downloading.

I wrote all the programs strictly as illustrative examples for this book. You're free to use the source code anyway you like, but bear in mind that this is not fully tested, commercial-quality code. Neither Prentice Hall nor I can be responsible for anything bad that may happen if you use these programs.

Although creating this book was primarily a solitary activity, I must acknowledge the help I got from several longtime good friends. Steve Drach, Bob Nicholson, and Owen Densmore tried out my demo applets to let me know whether they were any good and whether they ran properly in different browsers on various machine platforms (PCs, Macintoshes, and Sun workstations). Steve and I had a couple days of fun seeing how fast I could get my p programs to run.

I give extra special thanks to my technical reviewer, Wes Mitchell, another longtime friend who is currently an enterprise architect extraordinaire and formerly a mathematics and computer science professor. Wes made many suggestions for improving the text and caught some really embarrassing misstatements. (Any remaining errors are intentional—I want to see if you're paying attention.)

My agent from Waterside Productions, Danielle Jatlow, and my editor at Prentice Hall, Paul Petralia, got this project underway and kept it going.

I had a lot of fun writing this book and its programs, and I hope that comes through in the text. If you're inspired to learn more about any of the topics, then I will be very happy. You can send me e-mail at ron@apropos-logic.com or write to me at

Apropos Logic
P.O. Box 20884
San Jose, CA 95160

Edition details

• Publisher: Prentice Hall
• Publication date: 2002
• Language: English
• ISBN 10: 0130460419
• ISBN 13: 9780130460417
• Binding: Paperback
• Edition number: 1
• Number of pages: 480