A Numerical Library in C for Scientists and Engineers  book cover
1st Edition

A Numerical Library in C for Scientists and Engineers

ISBN 9780849373763
Published November 23, 1994 by CRC Press
816 Pages

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Book Description

This extensive library of computer programs-written in C language-allows readers to solve numerical problems in areas of linear algebra, ordinary and partial differential equations, optimization, parameter estimation, and special functions of mathematical physics.The library is based on NUMAL, the program assemblage developed and used at the Centre for Mathematics and Computer Science in Amsterdam, one of the world's leading research centers. The important characteristic of the library is its modular structure. Because it is highly compact, it is well-suited for use on personal computers.The library offers the expert a prodigious collection of procedures for implementing numerical methods. The novice can experiment with the worked examples provided and use the more comprehensive procedures to perform mathematical computations. The library provides a powerful research tool for computer scientists, engineers, and applied mathematicians. Applicable materials can be downloaded from the CRC Press website.

Table of Contents

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
Transformations 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
Numerical Differentiation
Analytic Problems
Non-Linear 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
Interpolations and Approximation
Real Data in One Dimension
Worked Examples
Prototype Declarations
Procedure Descriptions
Memory Management Utilities
Index of Procedures

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Lau, Hang T.