Java Number Cruncher: The Java Programmers Guide to Numerical Computing
Java Number Cruncher: The Java Programmers Guide to Numerical Computing
ISBN: 0130460419
EAN: 2147483647
EAN: 2147483647
Year: 2001
Pages: 141
Pages: 141
Authors: Ronald Mak
- 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
- 9.3 Identity Matrix
- 9.4 Row Vector
- 9.5 Column Vector
- 9.6 Graphic Transformation Matrices
- 9.7 A Tumbling Cube in 3-D Space
- References
- Chapter 10. Solving Systems of Linear Equations
- 10.1 The Gaussian Elimination Algorithm
- 10.2 Problems with Gaussian Elimination
- 10.3 Partial Pivoting
- 10.4 Scaling
- 10.5 LU Decomposition
- 10.6 Iterative Improvement
- 10.7 A Class for Solving Systems of Linear Equations
- 10.8 A Program to Test LU Decomposition
- 10.9 Polynomial Regression
- References
- Chapter 11. Matrix Inversion, Determinants, and Condition Numbers
- 11.1 The Determinant
- 11.2 The Inverse
- 11.3 The Norm and the Condition Number
- 11.4 The Invertible Matrix Class
- 11.5 Hilbert Matrices
- 11.6 Comparing Solution Algorithms
- References
- Part IV: The Joys of Computation
- Chapter 12. Big Numbers
- 12.1 Big Integers
- 12.2 A Very Large Prime Number
- 12.3 Big Integers and Cryptography
- 12.4 Big Decimal Numbers
- 12.5 Big Decimal Functions
- References
- Chapter 13. Computing p
- 13.1 Estimates of p and Ramanujan s Formulas
- 13.2 Arctangent Formulas That Generate p
- 13.3 Generating Billions of Digits
- References
- Chapter 14. Generating Random Numbers
- 14.1 Pseudorandom Numbers
- 14.2 Uniformly Distributed Random Numbers
- 14.3 Normally Distributed Random Numbers
- 14.4 Exponentially Distributed Random Numbers
- 14.5 Monte Carlo, Buffon s Needle, and p
- References
- Chapter 15. Prime Numbers
- 15.1 The Sieve of Eratosthenes and Factoring
- 15.2 Congruences and Modulo Arithmetic
- 15.3 The Lucas Test
- 15.4 The Miller-Rabin Test
- 15.5 A Combined Primality Tester
- 15.6 Generating Prime Numbers
- 15.7 Prime Number Patterns
- References
- Chapter 16. Fractals
- 16.1 Fixed-Point Iteration and Orbits
- 16.2 Bifurcation and the Real Function f(x)x2 c
- 16.3 Julia Sets and the Complex Function f(z)z2 c
- 16.4 Newton s Algorithm in the Complex Plane
- 16.5 The Mandelbrot Set
Java Number Cruncher: The Java Programmers Guide to Numerical Computing
ISBN: 0130460419
EAN: 2147483647
EAN: 2147483647
Year: 2001
Pages: 141
Pages: 141
Authors: Ronald Mak