Category list

Java Number Cruncher: The Java Programmer s Guide to Numerical Computing

Java Number Cruncher: The Java Programmer's Guide to Numerical Computing
By Ronald Mak

Publisher	: Prentice Hall PTR
Pub Date	: October 29, 2002
ISBN	: 0-13-046041-9
Pages	: 480
Supplier	: tEAm FLY

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.



	Table of Contents

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

By Ronald Mak

Publisher

: Prentice Hall PTR

Pub Date

: October 29, 2002

ISBN

: 0-13-046041-9

Pages

: 480

Supplier

: Team FLY

Preface

How to Download the Source Code

Part I. Why Good Computations Go Bad

Chapter 1. Floating-Point Numbers Are Not Real!

Section 1.1. Roundoff Errors

Section 1.2. Error Explosion

Section 1.3. Real Numbers versus Floating-Point Numbers

Section 1.4. Precision and Accuracy

Section 1.5. Disobeying the Laws of Algebra

Section 1.6. And What about Those Integers?

References

Chapter 2. How Wholesome Are the Integers?

Section 2.1. The Integer Types and Operations

Section 2.2. Signed Magnitude versus Two's-Complement

Section 2.3. Whole Numbers versus Integer Numbers

Section 2.4. Wrapper Classes

Section 2.5. Integer Division and Remainder

Section 2.6. Integer Exponentiation

References

Chapter 3. The Floating-Point Standard

Section 3.1. The Floating-Point Formats

Section 3.2. Denormalized Numbers

Section 3.3. Decomposing Floating-Point Numbers

Section 3.4. The Floating-Point Operations

Section 3.5. ±0, ±

, and NaN

Section 3.6. No Exceptions!

Section 3.7. Another Look at Roundoff Errors

Section 3.8. Strict or Nonstrict Floating-Point Arithmetic

Section 3.9. The Machine Epsilon

Section 3.10. Error Analysis

References

Part II. Iterative Computations

Chapter 4. Summing Lists of Numbers

Section 4.1. A Summing Mystery ”the Magnitude Problem

Section 4.2. The Kahan Summation Algorithm

Section 4.3. Summing Numbers in a Random Order

Section 4.4. Summing Addends with Different Signs

Section 4.5. Insightful Computing

Section 4.6. Summation Summary

References

Chapter 5. Finding Roots

Section 5.1. Analytical versus Computer Solutions

Section 5.2. The Functions

Section 5.3. The Bisection Algorithm

Section 5.4. The Regula Falsi Algorithm

Section 5.5. The Improved Regula Falsi Algorithm

Section 5.6. The Secant Algorithm

Section 5.7. Newton's Algorithm

Section 5.8. Fixed-Point Iteration

Section 5.9. Double Trouble with Multiple Roots

Section 5.10. Comparing the Root-Finder Algorithms

References

Chapter 6. Interpolation and Approximation

Section 6.1. The Power Form versus the Newton Form

Section 6.2. Polynomial Interpolation Functions

Section 6.3. Divided Differences

Section 6.4. Constructing the Interpolation Function

Section 6.5. Least-Squares Linear Regression

Section 6.6. Constructing the Regression Line

References

Chapter 7. Numerical Integration

Section 7.1. Back to Basics

Section 7.2. The Trapezoidal Algorithm

Section 7.3. Simpson's Algorithm

References

Chapter 8. Solving Differential Equations Numerically

Section 8.1. Back to Basics

Section 8.2. A Differential Equation Class

Section 8.3. Euler's Algorithm

Section 8.4. A Predictor-Corrector Algorithm

Section 8.5. The Fourth-Order Runge-Kutta Algorithm

References

Part III. A Matrix Package

Chapter 9. Basic Matrix Operations

Section 9.1. Matrix

Section 9.2. Square Matrix

Section 9.3. Identity Matrix

Section 9.4. Row Vector

Section 9.5. Column Vector

Section 9.6. Graphic Transformation Matrices

Section 9.7. A Tumbling Cube in 3-D Space

References

Chapter 10. Solving Systems of Linear Equations

Section 10.1. The Gaussian Elimination Algorithm

Section 10.2. Problems with Gaussian Elimination

Section 10.3. Partial Pivoting

Section 10.4. Scaling

Section 10.5. LU Decomposition

Section 10.6. Iterative Improvement

Section 10.7. A Class for Solving Systems of Linear Equations

Section 10.8. A Program to Test LU Decomposition

Section 10.9. Polynomial Regression

References

Chapter 11. Matrix Inversion, Determinants, and Condition Numbers

Section 11.1. The Determinant

Section 11.2. The Inverse

Section 11.3. The Norm and the Condition Number

Section 11.4. The Invertible Matrix Class

Section 11.5. Hilbert Matrices

Section 11.6. Comparing Solution Algorithms

References

Part IV. The Joys of Computation

Chapter 12. Big Numbers

Section 12.1. Big Integers

Section 12.2. A Very Large Prime Number

Section 12.3. Big Integers and Cryptography

Section 12.4. Big Decimal Numbers

Section 12.5. Big Decimal Functions

References

Chapter 13. Computing p

Section 13.1. Estimates of p and Ramanujan's Formulas

Section 13.2. Arctangent Formulas That Generate p

Section 13.3. Generating Billions of Digits

References

Chapter 14. Generating Random Numbers

Section 14.1. Pseudorandom Numbers

Section 14.2. Uniformly Distributed Random Numbers

Section 14.3. Normally Distributed Random Numbers

Section 14.4. Exponentially Distributed Random Numbers

Section 14.5. Monte Carlo, Buffon's Needle, and p

References

Chapter 15. Prime Numbers

Section 15.1. The Sieve of Eratosthenes and Factoring

Section 15.2. Congruences and Modulo Arithmetic

Section 15.3. The Lucas Test

Section 15.4. The Miller-Rabin Test

Section 15.5. A Combined Primality Tester

Section 15.6. Generating Prime Numbers

Section 15.7. Prime Number Patterns

References

Chapter 16. Fractals

Section 16.1. Fixed-Point Iteration and Orbits

Section 16.2. Bifurcation and the Real Function f ( x ) = x ² + c

Section 16.3. Julia Sets and the Complex Function f ( z ) = z ² + c

Section 16.4. Newton's Algorithm in the Complex Plane

Section 16.5. The Mandelbrot Set

References

Top

Flylib.com

Category list

Java Number Cruncher: The Java Programmer s Guide to Numerical Computing

Similar products

Similar products