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

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## B. Noble:

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

Published $\text {1964}$, **Oliver and Boyd Ltd**.

### Subject Matter

### 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