Book:B. Noble/Numerical Methods/Volume 1

Subject Matter

 * Numerical Analysis

Contents

 * PREFACE


 * I. ACCURACY AND ERROR
 * 1.1 Introduction
 * 1.2 Rounding off
 * 1.3 Absolute and relative errors
 * 1.4 Error analysis and control
 * 1.5 The evaluation of formulae on desk machines
 * 1.6 Mistakes
 * Examples I


 * II. ITERATIVE METHODS, WITH APPLICATIONS TO THE SOLUTION OF EQUATIONS
 * 2.1 Introduction
 * 2.2 A simple iterative method
 * 2.3 The Newton-Raphson iterative method
 * 2.4 General aspects of iterative procedures
 * 2.5 Real roots of polynomials
 * 2.6 Errors when finding roots of polynomials
 * 2.7 Bairstow's method for finding complex roots of polynomials
 * Examples II


 * III. ELEMENTARY PROGRAMMING FOR AUTOMATIC COMPUTERS
 * 3.1 Introduction
 * 3.2 Simple programs
 * 3.3 Some programs involving iterative procedures
 * 3.4 General comments
 * Examples III


 * IV. SIMULTANEOUS LINEAR ALGEBRAIC EQUATIONS
 * 4.1 Introduction
 * 4.2 The method of successive elimination
 * 4.3 Choice of pivots and scaling
 * 4.4 Inherent error and ill-conditioned equations
 * 4.5 A computer program for the method of successive elimination
 * Examples IV


 * V. MATRIX METHODS
 * 5.1 Matrix algebra
 * 5.2 A compact elimination method for the solution of linear equations
 * 5.3 The inverse matrix
 * Examples V


 * VI. EIGENVALUES AND EIGENVECTORS
 * 6.1 Introduction
 * 6.2 An iterative method for finding the largest eigenvalue
 * 6.3 The determination of subdominant eigenvalues and eigenvectors
 * 6.4 The iterative solution of linear simultaneous algebraic equations
 * Examples VI


 * INDEX