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Java Number Cruncher: The Java Programmers Guide to Numerical Computing
Java Number Cruncher: The Java Programmers Guide to Numerical Computing
ISBN: 0130460419
EAN: 2147483647
Year: 2001
Pages: 141
Authors:
Ronald Mak
BUY ON AMAZON
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
Year: 2001
Pages: 141
Authors:
Ronald Mak
BUY ON AMAZON
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