1st Edition

A Numerical Library in Java for Scientists and Engineers

By Hang T. Lau Copyright 2003
    1088 Pages
    by Chapman & Hall

    At last researchers have an inexpensive library of Java-based numeric procedures for use in scientific computation. The first and only book of its kind, A Numeric Library in Java for Scientists and Engineers is a translation into Java of the library NUMAL (NUMerical procedures in ALgol 60).

    This groundbreaking text presents procedural descriptions for linear algebra, ordinary and partial differential equations, optimization, parameter estimation, mathematical physics, and other tools that are indispensable to any dynamic research group.

    The book offers test programs that allow researchers to execute the examples provided; users are free to construct their own tests and apply the numeric procedures to them in order to observe a successful computation or simulate failure. The entry for each procedure is logically presented, with name, usage parameters, and Java code included.

    This handbook serves as a powerful research tool, enabling the performance of critical computations in Java. It stands as a cost-efficient alternative to expensive commercial software package of procedural components.

    INTRODUCTION
    ELEMENTARY PROCEDURES
    Real Vector and Matrix - Initialization
    Real Vector and Matrix - Duplication
    Real Vector and Matrix - Multiplication
    Real Vector Vector Products
    Real Matrix Vector Products
    Real Matrix Matrix Products
    Real Vector and Matrix - Elimination
    Real Vector and Matrix - Interchanging
    Real Vector and Matrix - Rotation
    Real Vector and Matrix - Norms
    Real Vector and Matrix - Scaling
    Complex Vector and Matrix - Multiplication
    Complex Vector and Matrix - Scalar Products
    Complex Vector and Matrix - Elimination
    Complex Vector and Matrix - Rotation
    Complex Vector and Matrix - Norms
    Complex Vector and Matrix - Scaling
    Complex Monadic Operations
    Complex Dyadic Operations
    Long Integer Arithmetic
    ALGEBRAIC EVALUATIONS
    Evaluation of Polynomials in Grunert Form
    Evaluation of General Orthogonal Polynomials
    Evaluation of Chebyshev Polynomials
    Evaluation of Fourier Series
    Evaluation of Continued Fractions
    Transformation of Polynomial Representation
    Operations on Orthogonal Polynomials
    LINEAR ALGEBRA
    Full Real General Matrices
    Real Symmetric Positive Definite Matrices
    General Real Symmetric Matrices
    Real Full Rank Overdetermined Systems
    Other Real Matrix Problems
    Real Sparse Non-Symmetric Band Matrices
    Real Sparse Non-Symmetric Tridiagonal Matrices
    Sparse Symmetric Positive Definite Band Matrices
    Symmetric Positive Definite Tridiagonal Matrices
    Sparse Real Matrices - Iterative Methods
    Similarity Transformation
    Other Transformations
    The (Ordinary) Eigenvalue Problem
    The Generalized Eigenvalue Problem
    Singular Values
    Zeros of Polynomials
    ANALYTIC EVALUATIONS
    Evaluation of an Infinite Series
    Quadrature
    Numerical Differentiation
    ANALYTIC PROBLEMS
    Nonlinear Equations
    Unconstrained Optimization
    Overdetermined Nonlinear Systems
    Differential Equations - Initial Value Problems
    Two Point Boundary Value Problems
    Two-Dimensional Boundary Value Problems
    Parameter estimation in differential equations
    SPECIAL FUNCTIONS
    Elementary Functions
    Exponential Integral
    Gamma Function
    Error Function
    Bessel Functions of Integer Order
    Bessel Functions of Real Order
    INTERPOLATION AND APPROXIMATION
    Real Data in One Dimension
    ADDENDA
    Fast Fourier Transforms
    Time Series Analysis
    WORKED EXAMPLES
    Examples for Chapter 1 Procedures
    Examples for Chapter 2 Procedures
    Examples for Chapter 3 Procedures
    Examples for Chapter 4 Procedures
    Examples for Chapter 5 Procedures
    Examples for Chapter 6 Procedures
    Examples for Chapter 7 procedures
    APPENDIX A: REFERENCES
    APPENDIX B: PROCEDURES DESCRIPTION
    INDEX OF PROCEDURES

    Biography

    Hang T. Lau (Author)