ProofWiki:Books/B. Noble/Numerical Methods 1: Iteration, Programming and Algebraic Equations

B. Noble: Numerical Methods 1: Iteration, Programming and Algebraic Equations

Published 1964, Oliver and Boyd Ltd.

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