# Book: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.

### 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
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