Java Number Cruncher: The Java Programmers Guide to Numerical Computing - page 1
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- Java Number Cruncher: The Java Programmer s Guide to Numerical Computing
- Java Number Cruncher: The Java Programmer s Guide to Numerical Computing
- Table of Contents
- Copyright
- Preface
- How to Download the Source Code
- Part I: Why Good Computations Go Bad
- Chapter 1. Floating-Point Numbers Are Not Real
- 1.1 Roundoff Errors
- 1.2 Error Explosion
- 1.3 Real Numbers versus Floating-Point Numbers
- 1.4 Precision and Accuracy
- 1.5 Disobeying the Laws of Algebra
- 1.6 And What about Those Integers?
- References
- Chapter 2. How Wholesome Are the Integers?
- 2.1 The Integer Types and Operations
- 2.2 Signed Magnitude versus Two s-Complement
- 2.3 Whole Numbers versus Integer Numbers
- 2.4 Wrapper Classes
- 2.5 Integer Division and Remainder
- 2.6 Integer Exponentiation
- References
- Chapter 3. The Floating-Point Standard
- 3.1 The Floating-Point Formats
- 3.2 Denormalized Numbers
- 3.3 Decomposing Floating-Point Numbers
- 3.4 The Floating-Point Operations
- 3.5 0, , and NaN
- 3.6 No Exceptions
- 3.7 Another Look at Roundoff Errors
- 3.8 Strict or Nonstrict Floating-Point Arithmetic
- 3.9 The Machine Epsilon
- 3.10 Error Analysis
- References
- Part II: Iterative Computations
- Chapter 4. Summing Lists of Numbers
- 4.1 A Summing Mystery?athe Magnitude Problem
- 4.2 The Kahan Summation Algorithm
- 4.3 Summing Numbers in a Random Order
- 4.4 Summing Addends with Different Signs
- 4.5 Insightful Computing
- 4.6 Summation Summary
- References
- Chapter 5. Finding Roots
- 5.1 Analytical versus Computer Solutions
- 5.2 The Functions
- 5.3 The Bisection Algorithm
- 5.4 The Regula Falsi Algorithm
- 5.5 The Improved Regula Falsi Algorithm
- 5.6 The Secant Algorithm
- 5.7 Newton s Algorithm
- 5.8 Fixed-Point Iteration
- 5.9 Double Trouble with Multiple Roots
- 5.10 Comparing the Root-Finder Algorithms
- References
- Chapter 6. Interpolation and Approximation
- 6.1 The Power Form versus the Newton Form
- 6.2 Polynomial Interpolation Functions
- 6.3 Divided Differences
- 6.4 Constructing the Interpolation Function
- 6.5 Least-Squares Linear Regression
- 6.6 Constructing the Regression Line
- References
- Chapter 7. Numerical Integration
- 7.1 Back to Basics
- 7.2 The Trapezoidal Algorithm
- 7.3 Simpson s Algorithm
- References
- Chapter 8. Solving Differential Equations Numerically
- 8.1 Back to Basics
- 8.2 A Differential Equation Class
- 8.3 Euler s Algorithm
- 8.4 A Predictor-Corrector Algorithm
- 8.5 The Fourth-Order Runge-Kutta Algorithm
- References
- Part III: A Matrix Package
- Chapter 9. Basic Matrix Operations
- 9.1 Matrix
- 9.2 Square Matrix
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