A Numerical Library in C for Scientists and Engineers: 1st Edition (Hardback) book cover

A Numerical Library in C for Scientists and Engineers

1st Edition

By Hang T. Lau

CRC Press

816 pages

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Hardback: 9780849373763
pub: 1994-11-23
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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

About the Series

Symbolic & Numeric Computation

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Number Systems