Table of Contents

 

	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		Copyright
		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