基本説明
Includes the latest version of BzzMath Library on CD-ROM, installation tutorial, all examples and sample codes described in the book as well as a host of additional examples.
Full Description
A practical engineer's companion to using numerical methods for the solution of complex mathematical problems. It thus enables readers to use and implement standard numerical tools in their work, explaining the theory behind the various functions and problem solvers, while showcasing applications in diverse scientific and engineering fields.
The material is based on several tried-and-tested courses for scientists and engineers taught by the authors, and all the exercises and problems are classroom-tested.
The required software is freeware developed and maintained by the authors, included on the accompanying CD-ROM, together with an installation tutorial, all the examples and sample codes described in the book, as well as a host of additional examples.
Contents
Preface
BASIC CONCEPTS
Introduction
Modeling Physical Phenomena
Number Representation on the Computer
Elementary Operations
Error Sources
Error Propagation
Decision-Making for an Optimal Program
Selection of Programming Languages: Why C++?
SOME UTILITIES IN THE BzzMATH LIBRARY
Introduction
Messages and Printing
Save and Load
Integer Algebra
BzzVevtorIntArray and BzzVectorArray
BzzMatrixCoefficientsExistence
BzzMatrixExistence
BzzSymmetricMatrixCoefficientsExistence
Complex Numbers
Miscellaneous Utilities
BzzPlot.exe and BzzPlotSparse.exe
LINEAR ALGEBRA
Introduction
Classes for Linear Algebra
BzzVector Class
BzzMatrix Class
Vector and Matrix Norms
Structured Matrices
Sparse Unstructured Matrices
Symmetric Matrices
Linear Algebra Operations
SQUARE LINEAR SYSTEMS
Introduction
Gauss Elimination
Gauss Transformation
Classical Gauss Factorization
Alternative Methods
Conditioning of Linear Systems
Best Pivot Selection
Solution Features
Class for Linear System Solution
Condition Number Computation
Determinant Evaluation
Inverse Matrix
Sparse Matrices
Classes for Linear System Solution with Sparse Unstructured Matrices
STRUCTURED LINEAR SYSTEMS
Introduction
Symmetric Matrices
Symmetric Sparse Matrices
Band Matrices
Diagonal Block Matrices
Iterative Methods
Systems Generated by Special Physical Problems
OVERDIMENSIONED LINEAR SYSTEMS
Introduction
Orthogonal Matrices
Problem Conditioning
Method of Least Squares
Orthogonal Transformation
QR Factorization
Classes for QRT Factorization
SVC Factorization
Class for SVD Factorization
Advantages of SVD Factorization
UNDERDIMENSIONED LINEAR SYSTEMS
Introduction
LQ Factorization
Classes for LQ Factorization
Null Space
Minimization with Linear Constraints
Minimizing a Sum of Squares Subject to Linear Constraints
Special Problems Solved by LQ Factorization
EIGENVALUES AND EIGENVECTORS FOR SYMMETRIC MATRICES
Introduction
Eigenvalues of Symmetric Matrices
Power Method
Inverse Power Method
Inverse-Translate Power Method
Jacobi Method
QR Algorithm
Eigenvalues of Rank-2 Matrices
ITERATIVE PROCESSES
Introduction
Convergence of an Iterative Algorithm
Convergence Speed
Convergence Accelerators
Extrapolation
Extrapolation Methods
Class for Numerical Derivation
APPENDIX A: Matrix Product
APPENDIX B: Entertainment
APPENDIX C: Basic Requirements for Using the BzzMath Library
APPENDIX D: Copyrights
